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THE)    VAN     NOSTRAND     SCIENCE     SERIES. 


o.    13.   GASES     MET    \VITH     IN     COAL     MINES. 

By  J.  J.  Atkinson.  Third  edition,  revised 
ai»d  enlarged,  to  which  is  added  The  Action 
of  Coal  Dusts  by  Edward  H.  Williams,  Jr. 

o.   14.   FRICTION   OP  AIR  IN  MINES.     By  J.  J. 

Atkinson.      Second    American    edition. 

o.   ir».    SKEW  ARCHES.      By  Prof.  E.  W.  Hyde, 

C.E.      Illustrated.  '    Seco.nd   edition. 

1C.   GRAPHIC       METHOD     'FOR       SOLVING 

Certain  Questions  in  Arithmetic  or  Algebra. 
By  Prof.  G.  L.  Vose.  Second  edition. 

]  o.  17.  WATER      AND       WATER-SUPPLY.       By 

Prof.  W.  H.  Corfield,  of  the  University  Col- 
lege, London.  Second  American  edition. 

13.    SEWERAGE      AND      SEWAGE     PUR1FI- 

cation.  By  M.  N.  Baker,  Associate  Editor 
"Engineering1  News."  Second  edition,  re- 
vised and  enlarged. 

<  O.   19.    STRENGTH          OF          BEAMS          UNDER 

Transverse  Loads.  By  Prof.  W.  Allan, 
author1  of  "Theory  of  Arches."  Second  edi- 
tion, revised. 

,o.  20.  BRIDGE    AND    TUNNEL    CENTRES.      By 

John  B.  McMaster,   C.E.      Second  edition.    •' 

/o.  21.  SAFETY  VALVES.     By  Richard  H.  Bael, 

C.E.     Third  edition. 

22.   HIGH  MASONRY  DAMS.     By  E.  Sherman 

Gould,  M.  Am.  Soc.  C.  'E.     Second  Edition. 

10.  23.   THE     FATIGUE     OF     METALS     UNDER 

Repeated  Strains.  With  various  Tables  of 
Results  and  Experiments.  From  the  Ger- 
man of  Prof.  Ludwig  Spangenburg,  with  a 
Preface  by  S.  H.  Shreve,  A.M. 

o.  24.  A  PRACTICAL   TREATISE  ON   THE 

Teeth  of  Wheels.  By  Prof.  S.  W.  Robinson. 
3d  edition,  revised,  with  additions. 

ro.  25.   THEORY        AND        CALCULATION        OF 

Cantilever  Bridges.     By  R.  M.  Wilcox. 

o.  2G.  PRACTICAL  TREATISE  ON  THE  PROP- 

erties  of  Continuous  Bridges.  By  Charles 
Bender,  C.E. 

o.  27.  BOILER   INCRUSTATION    AND    CORRO- 

sion.  By  F.  J.  Rowan.  Now  edition.  Re- 
vised and  partly  rewritten  by  F.  E.  Idell. 

o.  28.  TRANSMISSION    OF    POWTER   BY   WIRE 

Ropes.  By  Albert  W.  Stahl,  U.S.N.  Fourth 
edition,  revised. 


THE    VAN    NOSTRAND    SCIENCE    SERIES*. 

. ^ Jk 

No.  20.    STEAM     INJECTORS,     THEIR    THEORY 

and    Use.      Translated    from    the    French    by 
M.    Leon   Pochet. 

No.  30.   MAGNETISM  'OF    IRON    VESSELS^  AN?) 

Terrestrial    Magnetism.      By    Prof.    Falrman 
Rogers. 

No.  31.  THE    SANITARY    CONDITION    OF    CITY 

and    Country    Dx^lling--houses.      By    G^brge 
E.   Waring-,   Jr.      Second  edition,   revised. 

No.  32.   CABLE-MAKING       FOR        SUSPENSION 

Bridges.     B.  W.  Hildenbrand,  C.E. 

No.  33.  MECHANICS       OF      VENTILATION.      By 

George  W.  Rafter/  C.E. .    Second  edition;  re- 
vised. 

No.  34.  FOUNDATIONS.  By  Prof.  Jules  Gaudar^ 

C.E.      Translated   from   the   French.      Second 
edition. 

No.  35.  THE       ANEROID  BAROMETER:       ITS 

Construction  and  Use.  Compiled  by  Cffebrgre 

W.    Plympton.      Tenth  edition,    revised    and 
enlarged. 

No.  36.  MATTER    AND    MOTION.       By    J.     Clerk 

Maxwell,    M.A.      Second    American    edition. 

No.  37.  GEOGRAPHIC AL         SURVEYING:         ITS 

Uses,   Methods,    and   Results.      By   Frank   De 
Yeaux   Carpenter^C.E. 

No.  38.   MAXIMUM       STRESSES       IN       FRAMED 

Bridges.      By   Prof.   William   Cain,   A.M.,   C.E. 
New   and   revised   edition. 

No.  39.  A   HANDBOOK   OF   THE   ELECTRO- 

Magnetic      Telegraph.       By      A.     E.     Loring. 
Fourth  edition,  revised. 

No.  40.  TRANSMISSION    OF    POWER    BY    COM- 

pressed  Air.     By  Robert  Zahner,  M.E.     New 
edition,  in  press. 

No.  41.  STRENGTH  OF  MATERIALS.  By  Wil- 
liam Kent,  C.E.,  Asspc.  Editor  "Engineering 
News."  Second  edition. 

No.  42.  THEORY  OF  STEEL-CONCRETE 

Arches,  and  of  Vaulted  Structures.     By  Prof. 
Wm.    Cain.      Fourth   edition,    thoroughly   re- 
vised. 
No.  43.  \VAVE  AND  VORTEX  MOTION.     By  Dr. 

Thomas  Craig-,  of  Johns  Hopkins  University. 

No.  44.  TURBINE    WHEELS.       By    Prof.    W.    P. 

Trowbridge,   Columbia  College.      Second   edi- 
tion.    Revised. 


SUSPENSION    BRIDGES 
AND    CANTILEVERS 

THEIR  ECONOMIC  PROPORTIONS 
AND  LIMITING  SPANS 

Submitted  in  partial  fulfilment  of  the  requirements  for 
the  Degree  of  Doctor  of  Philosophy,  in  the  Faculty  of 
Pure  Science,  Columbia  University. 


D.  B.  STEINMAN,  C.E.,  PH.D. 

Assistant    Professor    of    Civil    Engineering    at  the 
University  of  Idaho. 


NEW  YORK 

D.    VAN    NOSTRAND    COMPANY, 

23  MURRAY  AND  27  WARREN  STREETS. 

1911. 


COPYRIGHT,   1911 

BY 
D.    VAN  NOSTRAND  COMPANY 


PBEFACE. 

In  recent  engineering  literature  there 
is  frequent  reference  to  the  question  of 
the  relative  adaptability  of  the  cantilever 
and  suspension  bridges  to  long  span  con- 
struction and  to  the  dearth  of  adequate 
data  from  which  the  limiting  and  eco- 
nomic spans  for  the  two  bridge-types 
might  be  deduced.  In  order  to  supply 
this  deficiency  and  to  determine  as  defi- 
nitely as  practicable  the  length  of  span 
at  which  the  suspension  bridge  becomes 
economically  superior  to  the  cantilever, 
the  author  has  undertaken  the  investiga- 
tions which  are  summarized  in  the  fol- 
lowing pages. 

In  connection  with  these  investiga- 
tions there  have  arisen  several  subsidiary 
problems  of  design.  It  was  found  nec- 
essary to  determine  the  economic  rise- 
ratio  for  suspension  bridges,  the  mini- 
mum depth  of  stiffening  trusses  for 

iii 

228654 


IV 

adequate  rigidity,  the  economic  depth  of 
stiffening  truss,  the  best  span-ratios  and 
the  minimum  width  for  cantilevers  and 
allied  questions  of  design  or  construction. 
The  solutions  of  these  problems,  together 
with  outlines  of  the  methods  of  designing 
the  different  parts  of  the  bridge  struc- 
tures are  included  in  this  book. 

The  author  desires  to  express  his  in- 
debtedness to  Professor  W.  H.  Burr  of 
Columbia  University  for  his  valuable  sug- 
gestions and  helpful  guidance,  to  Profes- 
sor C.  N".  Little  of  the  University  of  Idaho 
for  help  in  correcting  the  manuscript  and 
other  kind  assistance,  and  to  the  Depart- 
ment of  Bridges  of  New  York  City  for 
considerable  information  and  data  freely 
placed  at  the  author's  disposal. 

COLD  SPRING  ON  THE  HUDSON, 
August  1,  1911. 


CONTENTS 


CHAPTER  I. — INTRODUCTION 

ART.  PAGE 

1.  Statement  of   Problem    and    Proposed 

Method  of  Investigation 7 

CHAPTER  II. — STUDY  OF  SUSPENSION   BRIDGES 

2.  Suspension  Bridges — Notable  Spans ...  20 

3.  Wire  Cable  vs.  Eye-bars 22 

4.  Economic  Ratio  of  Rise  to  Span 35 

5.  Minimum    Depth     for    the    Stiffening 

Truss 50 

6.  Economic  Depth  of  Stiffening  Truss.  .  .  53 
Bibliography  on  Suspension  Bridges ...  59 

CHAPTER  III. — DESIGN  OF  SUSPENSION  BRIDGES 

7.  Principal  Data 65 

8.  Design  of  the  Stiffening  Truss 66 

9.  Design  of  Suspenders 80 

10.  Design  of  Cables 81 

11.  Design  of  Towers 85 

12    Design  of  Masonry  Piers 95 

v 


VI 


ART.  PAGE 

13.  Design  of  Anchorages 97 

14.  Estimates  of  Cost 99 

CHAPTER   IV. — CONCLUSIONS   FOR  SUSPENSION 
BRIDGES 

15.  Empiric  Formulae  for  Weights 106 

16.  Maximum  Span  for  Cable 109 

17.  Maximum  Span  for  Suspension  Bridges .    113 

18.  Empiric  Formula  for  Cost   of  Suspen- 

sion Bridges 119 

19.  Economic  Span  for  Suspension  Bridges.    120 

CHAPTER  V. — STUDY  OF  CANTILEVERS 

20.  Cantilever  Bridges — Historical   Sketch 

— Notable  Spans 129 

21.  Economic       Span-ratios       for      Canti- 

levers      136 

22.  Minimum  Width  for  Cantilevers 142 

Bibliography  on  Cantilevers 145 

CHAPTER  VI. — DESIGN  OF  CANTILEVERS 

23.  Principal  Data 149 

24.  Estimates  of  Cost 150 

CHAPTER  VII. — CONCLUSIONS  FOR  CANTILEVERS 

25.  Empiric  Formulae  for  Weights 157 

26.  Theoretical  Limiting  Spans  for  Canti- 

levers      161 

27.  Theoretical      Limiting     Span     for      a 

Simple  Truss 164 


vn 


ART.  PAGE 

28.  Maximum  Practicable  Span  for  Canti- 

levers    165 

29.  Empiric    Formula    for  Cost  of    Canti- 

levers     171 

30.  Economic  Span  for  Cantilevers    172 

CHAPTER    VIII. — FINAL      COMPARISONS      AND 
CONCLUSIONS 

31.  Costs     of     Suspension     Bridges    and 

Cantilevers 174 

32.  Span  of  Equal  Cost 177 

33.  Summary 181 

34.  Conclusions 183 


SUSPENSION  BRIDGES  AND 
CANTILEVERS 


CHAPTER  I 
INTRODUCTION 

ART.  1 

STATEMENT   OF   PROBLEM  AND   PRO- 
POSED METHOD  OF  INVESTIGATION 

EACH  type  of  bridge  construction 
has  some  limiting  span-length  which 
it  cannot,  physically,  exceed.  This 
maximum  span  may  be  defined  as  the 
length  at  which  the  ratio  of  the  intrinsic 
weight  to  the  applied  weight  becomes 
infinite.  In  other  words,  it  is  the 
length  at  which  the  structure  cannot 
carry  any  load  in  excess  of  its  own 

7 


weight ;  any  attempt  to  increase  the 
load  resulting  in  members  of  infinite 
cross-section.  Under  the  stress  of  neces- 
sity, the  span  of  any  type  of  bridge 
may  be  pushed  as  close  as  may  be 
desired  to  the  maximum  span-length; 
but  this  can  be  done  only  at  a  very 
great  sacrifice  of  economy,  as  the  cost 
of  the  structure  increases  very  rapidly 
when  the  span  approaches  the  limiting 
value.  The  length  of  the  maximum 
span  for  any  form  of  bridge  may  be 
determined  with  sufficient  definiteness 
from  theoretical  considerations  applied 
to  the  data  of  actual  designs;  but  it 
must  be  borne  in  mind  that  the  results 
of  such  determination  are  subject  to 
expansive  revision  when  the  methods 
of  design  or  the  materials  of  construc- 
tion undergo  improvement. 

In  addition  to  a  maximum  span- 
length,  each  bridge  type  has  an  economic 
range  of  spans,  within  which  it  will  be 
less  costly  than  any  other  form  of 
construction.  If,  for  any  two  com- 
parable types  of  structure,  a  span  of 


equal  cost  be  determined,  that  span 
will  be  the  inferior  economic  limit 
for  one  of  the  bridge-types  and  the 
superior  economic  limit  for  the  other. 

The  term  economic  span  will  be  used 
to  designate  the  span  at  which  the  cost 
of  a  bridge  would  exceed  the  cap- 
italized value  of  its  usefulness  to  the 
builders.  Although  this  is  a  problem 
of  great  practical  significance,  it  does 
not  lend  itself  to  accurate  treatment  in 
any  general  manner  owing  to  the  large 
possible  variations  in  local  conditions, 
such  as  the  magnitude  and  financial 
importance  of  the  traffic  expected, 
the  cost  of  real  estate  for  land  spans  and 
approaches,  and  the  difficulty  encoun- 
tered in  locating  suitable  foundations. 
The  results  of  a  general  determination 
of  the  economic  span,  as  here  defined, 
will  therefore  be  of  doubtful  practical 
value  except  for  purposes  of  illustra- 
tion or  comparison. 

The  maximum  and  economic  span- 
lengths  for  bridges  of  ordinary  span 
have  been  fixed  pretty  definitely  by 


10 


the  results  of  numerous  designs  and 
comparative  estimates.  We  may  take 
our  values  of  these  limiting  lengths 
from  the  consensus  of  opinion  among 
engineers  as  evidenced  by  their  uni- 
formity of  practice.  Thus  the  ordi- 
nary truss  bridge  finds  its  range  of 
usefulness  between  the  limiting  spans 
of  about  120  and  550  ft.,  there  being 
but  three  truss  spans  exceeding  the 
latter  value.  Below  this  range,  the 
steel  girder  or  concrete  arch  is  more 
economical;  above  these  limits  the 
steel  arch  enters  into  competition. 
The  latter  construction,  in  turn,  ceases 
to  be  economical  at  about  800  ft., 
although  the  proposed  Hell  Gate  Arch 
is  to  have  a  span  of  978  ft. 

For  longer  spans,  the  selection  of  a 
bridge  structure  narrows  down  to  a 
choice  between  the  suspension  bridge 
and  the  cantilever.  The  relative  econ- 
omy of  these  two  forms  of  construction 
has  long  been  a  mooted  question.  It 
is  true  that  the  longest  span  in  existence, 
viz.,  the  Forth  Bridge,  is  of  the  canti- 


11 

lever  type,  but  it  is  a  question  whether 
the  selection  of  this  type  was  not  a 
mistake.  "It  is  not  a  design  which 
would  ever  be  imitated.  Its  propor- 
tions are  very  injudiciously  taken, 
and  there  is  a  failure  to  reach  the  degree 
of  economy  which  ought  to  exist  even 
in  the  cantilever/71 

In  the  preliminary  investigations  for 
the  Quebec  Bridge,  the  Phoenix  Bridge 
Company  made  comparative  estimates 
of  a  cantilever  and  a  suspension  bridge 
for  the  ISOO-ft.  span.  "  Although  the 
cantilever  type  exhibited  the  more 
economic  results  of  the  two  as  the 
members  were  then  computed,  at  the 
present  time  the  economy  of  the 
adopted  type  is  not  so  clear  as  it  was 
originally  thought  to  be."2  The  col- 
lapse of  that  ill-fated  structure,  and  the 
investigations  following  the  completion 
of  the  Queensboro  Bridge  have  shaken 

1  W.  H.  Burr,  Proceedings  of  the  Engineers' 
Club  of  Philadelphia,  December,  1899. 

2  Editorial   in    Engineering  Record,    Sept.  5, 
1908. 


12 


the  general  confidence  in  the  cantilever 
type  of  construction  and  have  directed 
the  attention  of  engineers  to  the  more 
adequate  design  of  compression  mem- 
bers in  such  structures.  When  these 
members  are  designed  in  accordance 
with  the  recent  disclosures,  it  is  a 
question  whether  the  previously  ac- 
cepted economic  limit  for  cantilevers, 
viz.,  about  2000  ft.,  will  not  have  to 
be  considerably  reduced. 

The  limiting  economic  span  for  canti- 
levers is  placed  by  Prof /Burr  1  at  2000 
ft.  for  railway  bridges  and  at  1400-1600 
ft.  for  highway  bridges;  by  Prof. 
Merriman2  at  1500  ft.;  and  by  Prof. 
Melan 3  at  500  meters.  Gustav  Lin- 
denthal4  (M.  Am.  Soc.  C.E.)  would 

1  Proceedings    of    Engineers'   Club   of    Phil- 
adelphia, December,  1899.     Ancient  and  Modern 
Engineering  (New  York,  1903),  p.  177. 

2  Roofs  and  Bridges  (New  York,   1905),  Part 
IV,  pp.  110,  155. 

3  Handbuch       der       Ingenieur-Wissenschaften 
(Leipzig,  1906).     II.  Band,  V.  Abteilung,  s.  206. 

4  Engineering  (London),  December  19,  1890 
also  Proceedings  Am.  Soc.  C.  E.,  Sept.  21,  1904. 


13 


use  the  cantilever  for  spans  between 
500  and  2000  ft.,  the  steel  arch  between 
2000  and  4000  ft.,  and  the  suspension 
bridge  for  all  greater  spans.  Jos. 
Mayer  l  (M.  Am.  Soc.  C.E.)  considers  the 
minimum  economic  span  for  the  sus- 
pension type  to  be  800  ft.  for  highway 
bridges  and  1300  ft.  for  railway  bridges. 
No  mention  is  made  of  data  upon  which 
these  estimates  are  based. 

The  question  of  maximum  span  has 
also  been  under  discussion.  In  1894, 
a  prominent  bridge  engineer  declared 
before  a  congressional  committee  that 
"a  bridge  of  2800  ft,  would  be  just 
capable  of  holding  its  own  weight  with- 
out carrying  any  live  or  moving  load."  2 
A  few  months  later,  a  board  of  engineers 
approved  a  design  for  a  suspension 
bridge  of  3100-ft.  span  and  showed 
its  "  feasibility  of  manufacture  and 
cost.7'  This  Board,  appointed  by  act 
of  Congress  to  determine  the  prac- 
ticability of  a  long-span  bridge  across 

1  Proceedings  Am.  Soc.  C.  E.,  October,  1904. 

2  Engineering  Record,  Nov.  18,  1899. 


14 


the  Hudson  River  at  New  York  City, 
and  consisting  of  Major  C.  W.  Raymond, 
W.  H.  Burr,  G.  Bouscaren,  Theodore 
Cooper  and  Geo.  S.  Morison,  conducted 
a  series  of  investigations  and  reported 
that,  at  the  proposed  site,  a  2000-ft. 
clear-span  cantilever  could  be  built 
for  $27,000,000,  a  3100-ft.  clear-span 
cantilever  for  $51,000,000,  and  a  3100- 
ft.  clear-span  suspension  bridge  for 
$31,000,000.!  These  results  indicate 
that  the  maximum  practicable  limit 
for  suspension  bridges  is  above  3000  ft., 
and  that  the  economic  limit  for  canti- 
lever bridges  is  far  below  that  value. 

In  the  same  year  the  Secretary  of 
War  directed  the  formation  of  "  a 
Board  of  Officers  of  the  Engineer  Corps 
who  shall  investigate  and  report  their 
conclusions  as  to  the  maximum  length 
of  span  practicable  for  suspension 
bridges  and  consistent  with  an  amount 

1  Senate  Executive  Documents,  53d  Con- 
gress, 3d  Session,  No.  12,  Report  of  Board  of 
Engineers  on  the  N.  Y.  and  N.  J.  Bridge, 
Aug.  23d  1894. 


15 


of  traffic  probably  sufficient  to  warrant 
the  expense  of  construction/'  Assum- 
ing that  the  bridge  of  maximum  span 
is  supported  by  sixteen  2 IJ-inch  cables, 
and  has  to  carry  a  uniform  live-load 
of  27,540,000  Ibs.^L.  the  Board  ob- 
tained a  value  of  L  =  4335  ft.  for  the 
practical  maximum  span.1  The  above 
assumptions,  however,  were  rather  ar- 
bitrary; any  other  combination  of 
assumed  values  for  cable-section  and 
loading  would  have  resulted  in  a 
different  value  for  the  maximum  span- 
length. 

Although  comparative  designs  of  the 
two  types  of  long-span  bridges  have 
been  prepared  in  individual  instances 
for  the  particular  local  conditions 
obtaining,  the  writer  has  been  unable 
to  find  any  general  comparison  of  the 
two  bridge-types  for  the  purpose  of 
establishing  their  relative  economic  or 

1  Senate  Executive  Documents,  53d  Con- 
gress, 3d  Session,  No.  12,  Report  of  Board  of 
Engineer  Officers  to  Make  Investigations  of 
Certain  Bridges,  Sept.  29,  1894. 


16 

limiting  spans.  He  has  therefore  under- 
taken the  determination  of  these  values, 
namely : 

1.  The    maximum    practicable     span 
for  the  suspension-bridge  form  of  con- 
struction. 

2.  The    maximum    practicable    span 
for  cantilevers. 

3.  The  maximum  economic  span  for 
suspension  bridges. 

4.  The  maximum  economic  span  for 
cantilevers. 

5.  The   span   of   equal   cost   for   the 
two  types;    in  other  words,  the  span 
at  which  the   cantilever   ceases  to  be 
economically   superior   to   the    suspen- 
sion bridge. 

The  method  proposed  for  the  solu- 
tion of  these  problems  is  to  prepare 
designs  and  estimates  of  a  wide  range 
of  cantilevers  and  suspension  bridges 
and  to  deduce  therefrom  the  laws  of 
variation  of  weight  and  cost  with 
length  of  span.  The  relations  between 
span  and  weight,  thus  established,  will 
fix  the  maximum  feasible  span  for 


17 


each  form  of  construction.  The  cost- 
curves  of  the  two  types  will  indicate 
their  comparative  economy  at  different 
spans  as  well  as  the  critical  span  of 
equal  cost.  Finally,  an  estimate  of 
the  maximum  probable  traffic  returns  r 
compared  with  the  costs  of  different 
spans,  will  determine  the  economic 
limiting  length  for  each  type. 

The  cost  of  a  structure  for  a  given 
span  will,  of  course,  be  affected  by  local 
conditions  such  as  prices  of  material, 
specified  unit  stresses,  depth  of  founda- 
tions, etc.  In  order  that  the  com- 
parison between  the  cantilever  and  the 
suspension  bridge  may  be  an  absolutely 
fair  one,  it  is  essential  that  all  such 
arbitrary  or  varying  factors  be  chosen 
with  extreme  care  and  be  kept  exactly 
the  same  for  both  types  of  construc- 
tion. Furthermore,  in  order  that  the 
results  for  the  limiting  spans  may  be 
the  true  maximum  values,  it  is  neces- 
sary to  carefully  determine  and  use 
the  most  favorable  proportions,  material 
and  form  of  construction  for  each  design. 


18 


TABLE  I.— NOTABLE 


Date. 

Name. 

Location. 

Engineer. 

1903 

Williamsburg.  . 

EastR.,  N.  Y... 

L.  L.  Buck.  . 

1883 
1909 

1869 

Brooklyn  
Manhattan.  .  .  . 

i  Niagara 

EastR.,  N.  Y.... 
EastR.,  N.  Y.... 

Niagara  Falls 

Roebling  
Dept.  of  Br.  . 

Keefer 

1867 

Ohio  R 

Cincinnati  O 

Roebling 

1851 

2  Niagara 

Lewiston  N  Y 

Serrell 

1900 

Miampimi.  . 

Mexico      

1848 

3  Wheeling     . 

Ohio  R    W.  Va  . 

Ellet 

1903 
1834 

1855 
1899 

Elizabeth  
4  Freiburg  

Niagara  Ry  .  .  . 
Niagara    

Budapest  
Switzerland  

Niagara  Falls  .... 
Lewiston,  N.  Y  . 

Dept.  of  Br.  . 
Chaley  

Roebling  
R  S  Buck   . 

1900 

Rochester  

Ohio  R  ,  Pa 

1877 

s  Point 

Pittsburg 

Hemberle 

1902 

Vernaison 

France 

1896 

E  Liverpool    . 

Ohio        

1864 

Clifton 

Bristol  Eng 

1845 

Lancz     

'  Budapest        .... 

Clark     

1855 

Morgantown 

W  Virginia 

1825 

Menai 

Wales  

Telford    

1905 
1904 

Villefranche.  .  . 
Caperton  

France.  
W  Virginia    .... 

(Gisclard)  .  .  . 
Cooney  

1868 

6  Moldau 

Prague 

1852 

7  Charleston  .... 

W.  Virginia  

Ellet      

1818 

Tweed  
Grand  Ave.  .  .  . 

Berwick,  Eng.  .  .  . 
St  Louis  

Brown  

1862 

Lambeth      .  . 

London     

1826 

8  Conway 

Chester  Eng 

i  Strengthened  1888.     Wrecked  and  rebuilt  1889.     Re- 
placed by  arch  1896.  2  Removed  1864. 
3  Rebuilt  1854  and  1862.           4Two  cables  added  1881. 
5  Reconstructed   1905.                ^Rebuilt  with  cables  1900. 
?  Failed  1904.  8  Rebuilt  1904. 


19 


SUSPENSION  BRIDGES. 


Span. 

Rise 

Cables. 

Truss. 

Loading. 

=/ 

D  T, 

I 

h 

No. 

Size. 

D'p'h 

W't' 

L.L. 

D.L. 

HIT 

1600 

596 

177 

4 

181" 

40 

118 

6300 

16620 

2.6 

1595 

*930 

t!28 

4 

15| 

9,  17 

85 

2600 

8200 

3.2 

1470 

*725 

160 

4 

21i 

24 

122 

8000 

18000 

2.2 

1268 

1057 

*281 

t90 

4 

12* 

28 

52 

3600 

1042 

87 

8 

21 

1030 

-j- 

9 

5 

100 

300 

3  0 

1010 

4 

8 

951 

145 

95 

4 

20"E.B. 

23 

66 

5500 

14500 

2.6 

870 

174 

63 

6 

2,8 

5 

21 

821 

t54 

4 

10i 

16 

25 

1800 

1800 

1.0§ 

800 

34 

53 

4 

10 

14 

28 

2400 

2850 

1.3 

800 

•416 

72 

2 

7 

18 

800 

145 

88 

2 

8"E.B.J 

8 

34 

1700 

764 

*172 

f 

2 

4 

17 

680 

600 

O.ft 

705 

9 

7| 

702 

Chains 

663 

*285 

48 

4 

Chains 

608 

150 

42 

6 

31 

5 

20 

2000 

578 

*260 

43 

16 

Chains 

2500 

512 

128 

t 

2 

tWire 

0 

20 

2000 

2000 

1  0 

510 

# 

37 

2 

1ft 

0 

6 

120 

100 

482 

8 

Chains 

478 

25 

4 

0 

17 

450 

30 

12 

Chains 

400 

*150 

40 

4 

JChains 

60 

363 

.4. 

JChains 

327 

22 

Chains 

*  Provided  with  suspenders  in  side  spans. 

t  Stiffened  with  diagonal  stays. 

j  Braced  cable  construction. 

§  Railway  bridge.     Replaced  by  arch  in  1897. 


20 


CHAPTER  II 
STUDY   OF   SUSPENSION    BRIDGES 

ART.  2 
SUSPENSION  BRIDGES 

THE  economic  utilization  of  the  mate- 
rials of  construction  demands  that,  as 
far  as  possible,  the  predominating 
stresses  in  any  structure  should  be 
those  for  which  the  material  is  best 
adapted.  The  superior  economy  of 
steel  in  tension  and  the  uncertainties 
involved  in  the  design  of  large-sized 
compression  members  point  emphat- 
ically to  the  conclusion  that  the  mate- 
rial of  long-span  bridges,  for  economic 
designs,  must  be  found  to  the  greatest 
possible  extent  in  tensile  stress.  This 
requirement  is  best  fulfilled  by  the 
suspension-bridge  type. 

The    superior    economy    of   the   sus- 


21 


pension  type  for  long-span  bridges 
is  due  fundamentally  to  the  following 
causes: 

1.  The  very  direct  stress-paths  from 
the  points  of  loading  to  the  points  of 
support. 

2.  The  predominance  of  tensile  stress. 

3.  The     highly     increased     ultimate 
resistance  of  steel  in  the  form  of  cable- 
wire. 

With  the  exception  of  the  Forth 
Bridge,  the  Queensboro  Bridge  and  the 
Quebec  Bridge  (under  construction), 
all  structures  exceeding  1000  ft.  in 
span  have  been  suspension  bridges. 
Table  I  gives  a  list  of  the  most  notable 
structures  of  this  type,  with  their 
principal  dimensions.  It  is  seen  from 
this  table  that  all  suspension  bridges 
erected  after  what  might  be  called  the 
experimental  period  (1796-1876)  have  a 
minimum  span  of  about  800  ft.  and  a 
maximum  span  of  1600  ft. 

In  order  to  secure  information  needed 
in  determining  the  maximum  and 
economic  spans  for  suspension  bridges, 


22 


in  addition  to  the  data  supplied  by 
existing  structures,  the  writer  has 
undertaken  the  design  of  three  suspen- 
sion bridges,  having  span -lengths  of 
1500,  2250  and  3000  ft.,  respectively. 
To  justify  the  large  expenditure  in- 
volved in  structures  of  this  magnitude, 
they  will  be  assumed  to  be  railroad 
bridges,  with  additional  provision  for 
electric  cars,  driveway  and  footwalks. 
Before  we  can  proceed  with  the 
designing  of  the  structures,  it  is  nec- 
essary to  find  the  most  favorable 
solutions  of  the  following  problems: 

1.  The  choice  between  wire-cable  and 
•eye-bar  construction. 

2.  The  economic  ratio  of  cable-rise 
to  length  of  span. 

3.  The  best  ratio  of  depth  of  stiffen- 
ing truss  to  length  of  span. 

ART.  3 
WIRE  CABLE  vs.  EYE-BARS 

One    of    the    first    questions    to    be 
decided  in  the  design  of  a  suspension 


23 


bridge  is  the  choice  between  a  steel- 
wire  cable  and  a  chain  of  eye-bars  for 
the  principal  carrying  member.  The 
latter  enables  the  bracing  for  the  pre- 
vention of  deformation  under  moving 
load  to  be  incorporated  in  the  cable 
system;  the  other  requires  a  separate 
stiffening  truss  for  the  reduction  of 
these  deflections.  A  third  method  of 
bracing  the  suspension  bridge  against 
deformation  is  the  introduction  of 
diagonal  stays  between  the  towers  and 
the  roadway,  as  was  done  in  the  Ohio 
River,  Brooklyn  and  Vernaison  Bridges. 
This  method,  however,  has  been  aban- 
doned in  recent  designs  as  the  stays 
have  been  shown  to  be  of  doubtful 
utility  and,  furthermore,  fail  to  act 
in  unison  with  the  cable  and  suspen- 
ders under  changes  of  temperature. 
The  earliest  suspension  bridges  were 
built  with  chains.  James  Finley,  the 
pioneer  builder  of  suspension  bridges 
in  America,  used  common  wrought- 
iron  chains  for  all  of  his  bridges  from 
the  70-ft,  span  at  Uniontown,  Pa. 


24 

(1796),  up  to  his  greatest  achievement, 
the  309-ft.  span  of  the  Schuylkill 
Bridge  (1808).  In  1818,  Brown  sub- 
stituted a  chain  of  eye-bars,  bolted 
together,  in  building  the  Tweed  Bridge 
of  450-ft.  span.  This  construction 
was  followed  in  the  Menai  Bridge, 
built  by  Telford  in  1825,  and  the 
Hammersmith  Bridge  (London)  built 
by  Clark  in  1827.  The  following  year 
an  advance  was  marked  by  the  use 
of  open-hearth  steel  for  the  chains 
of  the  Karl  Bridge  at  Vienna  (312 
ft.  span).  Steel  eye-bar  chains  re- 
mained in  use  for  bridges  of  constantly 
increasing  span,  including  Brunei's 
Hungerford  Bridge  (London,  1845), 
Clark's  Bridge  at  Budapest  of  663 
ft.  span  (1845),  and  the  Clifton  Bridge 
of  702  ft.  span  (Bristol,  1864). 

In  the  meantime,  John  A.  Roebling 
was  at  work  at  Saxonburg,  Pa.,  invent- 
ing and  developing  the  manufacture 
of  wire  rope.  He  soon  conceived  the 
possibility  of  its  application  in  the 
construction  of  suspension  bridges,  in 


25 


place  of  the  eye-bar  chains,  on  account 
of  its  superior  strength  and  ease  of 
erection.  Beginning  with  the  use  of 
wire  cable  for  the  suspension  of  canal 
aqueducts,  he  proceeded  to  apply  it 
to  more  ambitious  structures.  In  1848, 
Chas.  Ellet  built  the  wire-cable  bridge 
over  the  Ohio  River  at  Wheeling  with  a 
span  of  1010  ft.  which  was  blown  down 
in  1854.  In  1851,  Roebling  commenced 
his  821-ft.  suspension  bridge  over 
Niagara  Falls,  the  first  and  only  sus- 
pension structure  to  be  built  for  heavy 
railroad  traffic.  In  1867,  he  completed 
the  Covington  and  Cincinnati  Bridge 
over  the  Ohio  River,  with  a  span  of 
1057  ft.  These  achievements  of  Roeb- 
ling, however,  were  but  a  preliminary 
training  for  "  the  monumental  work 
that  was  to  cost  him  his  life  while 
crowning  it  with  glory."  When  he 
presented  his  plans  for  spinning  his 
steel  wires  over  the  vast  span  of  the 
Brooklyn  Bridge,  he  had  to  defend 
his  ideas  against  the  scoffing  of  the 
whole  world  and  had  to  fight  his 


26 


opponents  inch  by  inch  before  the  right 
to  try  was  given  him.  The  bridge  was 
finished  by  his  son  in  1883,  and  held 
the  record  for  length  of  span  (1595.5  ft.) 
ujitil  the  Williamsburg  Bridge  (1600 
ft.)  was  completed  by  L.  L.  Buck  in 
1903.  With  the  third  span  across 
the  East  River,  the  Manhattan  Bridge 
of  1470  ft.  span,  opened  in  1909,  we  are 
brought  to  the  present  day  in  the  his- 
tory of  suspension  bridges. 

Since  the  time  of  Roebling,  wire 
cables  have  been  used  in  all  suspension 
bridges  with  but  one  exception:  the 
Elizabeth  Bridge  over  the  Danube  River 
at  Budapest  (1903).  Its  span  of 
951  ft.  is  the  largest  of  any  suspension 
bridge  outside  of  America. 

In  nearly  all  of  the  above  bridges,  a 
stiffening  truss  is  the  means  employed 
to  prevent  the  deformations  due  to 
live-load,  wind  and  changes  of  tem- 
perature. Another  practicable  method 
is  to  build  the  cable  as  a  trussed  struc- 
ture like  an  inverted  two-hinged  or 
three-hinged  arch.  This  method  was 


27 


used  in  the  Point  St,  Bridge  at  Pitts- 
burg  (span  =  800  ft.)  which  was  built 
by  Hemberle  in  1877.  In  this  bridge 
the  cable  is  composed  of  8-inch  eye- 
bars  and  is  trussed  on  its  upper  side 
by  bracing  connecting  it  to  two  straight 
chord-members  running  from  the  ends 
to  the  middle  of  the  cable. 

In  1894,  Gustav  Lindenthal  offered 
a  design  for  a  suspension  bridge  over 
the  Hudson  River,  with  a  clear-span 
of  3100  ft.,  in  which  he  used  two  pairs 
of  parallel  cables  connected  by  a  system 
of  bracing  in  a  vertical  plane.1  He 
proposed  building  the  cables  of  pin- 
connected  wire  links,  claiming  for  such 
construction  the  advantages  of  accurate 
work  and  close  inspection  in  the  shop, 
rapid  erection,  and  possibility  of  vary- 
ing the  cable-section  as  required. 

In  preparing  the  design  of  the  Man- 
hattan Bridge  over  the  East  River,  the 
New  York  Department  of  Bridges 
followed  LindenthaPs  scheme,  using 

1  Report  of  Board  of  Engineer  Officers  on 
the  N.  Y.  and  N.  J.  Bridge,  1894.  Appendix  D. 


28 


braced  cables  built  up  of  eye-bars. 
The  following  year,  with  a  change  of 
city  administration,  that  plan  was 
abandoned  and  the  structure  rede- 
signed with  wire  cables.  In  September, 
1904,  Lindenthal  explained  and  de- 
fended his  design  in  a  paper  read  before 
the  American  Society  of  Civil  Engineers,1 
which  gave  rise  to  a  long  series  of  very 
fruitful  discussions.2  The  principal 
advantages  claimed  for  the  two  types 
may  be  summarized  as  follows: 

ADVANTAGES    OF    THE     BRACED-CABLE 
TYPE  OF  SUSPENSION  BRIDGE 

1.  By  having  the  greatest  depth  of 
the  bracing  at  the  one-quarter  points, 
where  the  maximum  moments   occur, 
the  stiffness  of  the  bridge  with  a  given 
expenditure     of     material      is     greatly 
increased. 

2.  The  small  depth  along  the  middle 
third    of   the    span   reduces    the    tem- 
perature stresses. 

1  Transactions  Am.  Soc.  C.  E.,  Sept.  21,  1904. 

2  Ibid.,  Oct.,  1904  to  Mar.,  1905. 


29 


3.  The     stiffened-cable    construction 
saves  one  chord  of  the  truss  as  the  cable 
itself  forms  the  upper  chord. 

4.  The  section  of  an  eye-bar  chain 
may  be  varied  with  the  stress,  whereas 
the  entire  wire   cable  must  have  the 
maximum  section. 

5.  Greater    weight,    if    it    does    not 
increase  the  cost,  is  an  advantage  in  a 
bridge,    as    it    serves    to    increase    the 
rigidity  of  the  structure. 

6.  The  pin-connections  facilitate  the 
speedy  erection  of  the  cable. 

DISADVANTAGES  OF  THE  BRACED-CABLE 
TYPE 

1.  An  unpleasant  appearance  is  pro- 
duced by  the  lattice-work  up   in  the 
air. 

2.  Since   the   bottom   chords   of  the 
bracing  run  to  the  top  of  the  towers, 
special    wind-chords  at    the  floor-level 
become  necessary  for  lateral  stiffness, 
and  these  may  be  as  heavy  as  the  bot- 
tom chords  themselves. 

3.  It  is  impossible  to   calculate  the 


30 

stresses  accurately  on  account  of  the 
difficulty  in  adjusting  the  members. 
The  safe  working  stresses  should  there- 
fore be  reduced  by  at  least  5  per  cent. 

4.  The   braced-cable  type  exposes  a 
large  area  to  the  wind  at  the  highest 
elevation,  thereby    greatly    increasing 
the  wind-stresses  in  the  bracing  and  in 
the  towers. 

5.  If  the  floor  is  not  stiffened  verti- 
cally,    every     suspender     receives     a 
heavier   concentrated   load   and   every 
shock  from  moving  loads  is  transmitted 
directly  to  the  cables  instead  of  being 
absorbed  by  the  floor  system. 

6.  The    braced     system     introduces 
many    elements    of     uncertainty    and 
complexity  in  the  structure,  and    the 
history  of  bridge  design  shows  that  "  the 
lines    of    progress    have    been    in    the 
direction  of  eliminating  uncertain  ele- 
ments and  holding  fast  to  those  features 
which  secure   certainty    in  the    deter- 
mination of  stresses. " 

7.  The    practical    difficulty,    hazard 
and    expense    of    making    satisfactory 


31 


connections  between  a  cable  and  the 
web-members  of  an  overhead  bracing 
system  preclude  the  use  of  wire  cables, 
and  to  abandon  the  wire  cables  is  to 
abandon  all  the  essential  advantages 
of  the  suspension  bridge.  The  superior 
economy  of  the  wire  cable  over  eye-bar 
construction  rests  on  the  following 
considerations: 

(a)  Steel  wire  with  an  elastic  limit 
of  180,000  Ibs.  per  sq.in.,  is  obtainable 
at  a  cost  of  but  twice  as  much  per 
pound  as  nickel-steel  eye-bars  with 
one-fourth  the  elastic  limit.1 

(6)  The  eye-bar  heads  and  pins  add 
about  25  per  cent  to  the  weight  of  the 
cable. 

(c)  An  eye-bar  chain  will  therefore 
weigh  about  four  times  as  much,    and 
cost  about  twice  as  much    as  a  wire 
cable  to   carry  an  equal  load,   if  the 
same  factor  of  safety  is  to   be  main- 
tained. 

(d)  The    increased    dead-weight     of 

1  Cf.  R.  S.  Buck  and  Jos.  Mayer,  Trans. 
Am.  Soc.  C.  E.,  Oct.,  1904. 


32 


the  cable ,  when  eye-bars  are  used, 
results  in  increased  stresses  in  cable, 
towers  and  anchorages. 

(e)  The  wire  cable  is  self-supporting 
during  erection  and  all  the  problems 
involved  have  been  worked  out  and 
successfully  demonstrated.  The  eye- 
bars,  on  the  other  hand,  would  require 
a  temporary  supporting  cable;  and 
the  manufacture  and  erection  of  eye- 
bars  of  suitable  size  for  very  long  spans 
present  many  unsolved  difficulties. 

Many  of  the  advantages  enumerated 
above,  particularly  those  bearing  on 
the  economy  of  the  respective  types, 
practically  balance  each  other,  so  that, 
in  consequence,  there  is  really  no  mate- 
rial difference  between  the  costs  of 
the  two  forms  of  construction.  In  a 
comparative  design  of  the  two  types 
for  a  proposed  bridge  at  Cologne,  of 
722  ft.  span,  O.  Erlinghagen  found  that 
the  eye-bar  chain  would  require  about 
twice  as  much  material  as  the  wire 
cable  but,  on  account  of  the  difference 
in  unit  prices,  the  total  cost  of  the  two 


33 


structures  was  almost  exactly  the 
same.1  Jos.  Mayer  (M.  Am.  Soc.  G.E.) 
compared  the  two  types  for  a  span  of 
3000  ft.,  and  found  the  braced-cable 
type  to  weigh  5000  Ibs.  more  per  linear 
foot  than  the  other.2  Prof.  J.  Melan 
found  the  difference  of  cost  between 
chain  and  cable  for  the  Elizabeth 
Bridge  at  Budapest  to  be  negligible, 
the  eye-bar  chain  being  adopted  for 
other  considerations.3  The  two  designs 
for  the  Manhattan  Bridge  showed  a 
difference  in  cost  of  7  per  cent  in  favor 
of  the  eye-bar  type,  although  the  chain 
in  the  latter  weighed  2^  times  as  much 
as  the  wire  cable.4 

Omitting  from  consideration  the  pos- 
sibility of  using  the  overhead  sys- 
tem of  bracing  in  conjunction  with 
a  wire  cable,  a  construction  which  would 
combine  the  essential  advantages  of 

1  R.  R.  Gazette,  Nov.  20,  1903. 

2  Transactions  Am.  Soc.  C.  E.,  Vol.  48,  p..' 
371.      - 

3  Transactions  Am.  Soc.  C.  E.,  Feb.,  1905. 
4 Engineer  (London),  Aug.  28, 1903. 


34 


both  systems  but  of  which  the  feasibil- 
ity has  not  yet  been  demonstrated, 
and  without  presuming  to  decide  be- 
tween the  relative  advantages  of  the 
two  types  of  cable  construction,  the 
writer  will  adopt  the  wire-cable  type 
in  the  present  investigations  for  the 
following  reasons: 

1.  As    both    types    are    practically 
equal  in  cost,  this  choice  will  not  affect 
the  results  for  the  economic  lengths  of 
span. 

2.  As  the  wire  cable  affords  a  great 
saving  in  weight,  it  will  yield  a  larger 
value    for    the    maximum    practicable 
span. 

3.  As  this  choice  conforms  with  the 
accepted  past  and  present  practice  in 
suspension   bridge   design,    and    as   no 
radical  changes  need  be  expected  in  the 
proximate  future,  the  results  obtained 
will  be  better  adapted  for  comparison 
with  the    data    of   existing    structures 
and    of    greater   value   in    estimating 
future  designs. 


35 


ART.  4 
THE  ECONOMIC  RATIO  OF  RISE  TO  SPAN 

(a)  Cost  of  Cable.  Let  ft  =  the  ratio 
of  the  rise  (/)  to  the  span  (I)  of  the  cable. 
The  total  load  per  linear  foot  carried 
by  the  cable  consists  of  two  parts: 
#0  =  the  weight  of  the  cable  itself,  and 
<7i  =  the  weight  of  the  total  suspended 
(dead  and  live)  load.  As  is  well 
known,  if  a  is  the  inclination  of  the 
cable  at  the  towers,  the  maximum 
tension  in  the  cable  will  be 


(1) 


The  weight  of  the  cable  per  horizontal 
linear  foot  is  given  by 


(2) 


where  SQ  is  the  unit  working  stress  and 
fo  is  the  weight  per  linear  foot  per 
square  inch  of  cross-section.  Sub- 


36 

stituting  the  value  of  T  from  Eq.  (1), 
Eq.  (2)  may  be  written, 

flfo==^(sfo  +  9fi)  *Z — vl-f-16n2    .    (3) 

H 

where 

!)^7  •     •     •     W 


The  factor  (1  +  fn2),  for  all  practical 
values  of  n,  varies  only  from  the  value 
1.02  to  1.05;  hence  the  quantity  k 
may  be  considered  as  practically  in- 
dependent of  the  rise-ratio  n.  The 
solution  of  Eq.  (3)  gives 


(5) 


If  Z/o  =  the  total  horizontal  length  of 
cable  and  c0  =  the  cost  per  pound  of 
the  cable  material,  the  total  cost  of  the 
cable  will  be, 


37 

Substituting   the    value   of   gQ   from 
Eq.  (5),  we  obtain 

/c-vr+^ 

—    .     (6) 


-kl-> 
n 

where 

a=^-c0.        ...     (7) 

Numerical  Values.  Allowing  for  the 
weight  of  cable  wrapping,  a  mean  value 
for  ro  is  3.5.  Hence,  by  Eq.  (4),  for  a 
range  of 


we  may  take, 

0.455  f4t\ 

^  = .     .     .     (ft ) 

SQ 
If  c0  =15  cents  per  Ib.  and    y  has  its 

minimum  value  of  1.5  (for  no  suspenders 
in  side  spans) , 

a  =  22.5.        .     .     .     (70 


38 


If  the  side-spans  are  suspended,  —=2y 

6 

hence 

a  =  30.0  ....     (7") 

(b)  Cost  of  Suspension  Rods.  If  L2 
is  the  total  length  of  bridge  provided 
with  suspension  rods,  the  total  load 
carried  by  them  will  be  giL2.  Since 
the  cable  is  a  parabola,  the  average 
length  of  the  rods  is  //3.  If  $2 
is  the  unit  stress,  ^2  the  unit  weight, 
and  02  the  unit  cost,  the  total  cost  of 
the  rods  will  be 


^Z  *"JS  /  A      q 

This  may  be  written 
where 


Numerical  Values .     If  s2  =  30 ,000  Ibs . 
per   sq.in.,    7-2  =  3. 4,    c2  =  12    cents    per 


39 


lb.,    and    1/2/2=1    (i.e.   no    suspenders 
in  the  side-spans),  then 

b  =.00045.    .     .     .     (90 

L2 

If  -y  =2   (side-spans  suspended),  then 

b  =.00090.     .     .     .     (9") 

(c)  Cost  of  Towers.  With  the  entire 
bridge  fully  loaded,  the  total  compres- 
sion in  each  tower  will  be  twice  the 
end-shear  in  the  cable  or 

Ps  =  (g0+gi)-i.    .    .    (10) 

If  £3  is  the  working  intensity  of  stress, 
the  required  section  for  each  tower  is 

A,-£g-->  +  gl)*.  (11) 

S3  «3 

or,  substituting  the  value  of  gQ  from  Eq. 
(5), 

A.-21?  ---  J_—  -.     (12) 


Let  7-3  =  the  weight  per  linear  foot  of 
tower  per  square  inch  of  cross-section, 
c3  =  the  unit  cost  of  the  material,  T-/= 


40 


total  height  of  tower;    then  the  total 
cost  of  the  two  towers  will  be 


or,  substituting   the  value   of  A3  from 
Eq.  (12), 


,   (13) 


1 

1— kl—< 
n 

where 


Numerical  Values.  A  comparative 
study  of  existing  structures  yields 
the  following  mean  values  for  the 
constants:  7-5  =  6.5  (including  diagonal 
members,  details,  etc.),  c3  =  5.6  cents 
per  Ib.  (price  of  structural  steel  and 
erection),  s3=8000  Ibs.  per  sq.in.  (for 
the  direct  stress  exclusive  of  bending 
stresses),  r=1.6  (a  mean  value  for  the 
longer  spans).  With  these  values,  Eq. 
(14)  gives 

c=.0145.     ...     (140 


41 


Thus  far,  in  the  analysis,  there  is  noth- 
ing essentially  new.  We  now  pro- 
ceed to  apply  the  above  results  to  our 
immediate  purpose. 

Total  Cost.  The  total  cost  of  the 
structure,  exclusive  of  truss,  anchorages, 
substructure,  etc.  (which  are  inde- 
pendent of  n),  may  be  obtained  by 
adding  together  the  right-hand  members 
of  Eqs.  (6),  (8),  (13),  giving  the  result, 


or,  -expanding  the  radical, 


The  condition  for  a  minimum  total  cost 
then  becomes 


— 128afcn3 


I    .  (1  —  lo/cm  -r  LAOKM .  .; , 


]-«• 


42 


Clearing  of  fractions,  and  arranging 
the  terms  according  to  the  ascending 
powers  of  n,  we  obtain, 

(bkW-ak)-(2ckl+2bkl)n+(8ak+b+c+lGbkV)n* 
-(16&M)n3-(96afc)n4-f  .  .  .=0.      (16) 

It  may  be  readily  shown  that  the  terms 
containing  n3  or  higher  powers  of  n  are 
absolutely  negligible  in  comparison 
with  the  remaining  terms,  and  they  will 
therefore  be  dropped  from  the  equation. 
Solving  the  resulting  quadratic  equa- 
tion for  n,  we  obtain 


(b  +  c)2kl  ±  V  4  (6  +  c)dk  4-  32a2fc2 


(17) 

On  account  of  the  relatively  small 
values  of  b  and  &,  the  terms  containing 
bk2  and  b2k4  may  be  neglected  without 
any  appreciable  error  for  any  feasible 
length  of  span.  The  equation  is  thus 
simplified  to 


(18) 


43 


This  equation  shows: 

1.  That  the  economic  rise-ratio    (ri) 
increases  with  the  length  of  span. 

2.  That   the   economic   rise-ratio   in- 
creases with  any  increase  in  the  cable- 
factors   (a,  k)  and  decreases  with   any 
increase    in    the    tower-factor     (c)     or 
the    suspension-rod    factor     (6).       See 
Eqs.   (4),   (7),   (9),   (14). 

Substitution  of  Numeral  Values.  Case 
I.  No  suspenders  in  the  side-spans. 
By  Eqs.  (4')  (7'),  (9')  and  (14') 

k  =  —  b  =.00045. 

so 

a  =  22.5  c=.0145. 

Substituting  these  values  in  Eq.  (18), 
we  obtain 

.0299Z  ±^2.96180 +  16210 +  .0008676* 
.0658s0+360 

(18a) 

If  s0  =  60,000  Ibs.  per  sq.in.,  this  becomes 


44 


where  I  is  the  span-length  in  thousands 
of   feet.     Hence,  if 


7 i  nnn'   ^  —  110 

i ±UUU    ,     II •  -L  AV/ x-v     i 

2000',  n-  .118= JL  [  Economic  ratios 
8.5    of  rise  to  span. 

3000',  n=. 126=^ 

4000',  n  =.135  =  =-^ 

Case  //.     Suspended  side-spans. 
By  Eqs.  (4'),  (7'0,  (9")  and  (14'), 


so 


a  =  30 


c=.0145. 


Substituting  these  values  in  Eq.  (18), 
we  obtain 


.0308?  ±  \/4.06so  +  28,800  +  .000894Z2 


.0677s0 


(186) 


45 


If  s0  =  60,000  Ibs.  per  sq.in.,  this  becomes 
n=  .0068Z±  V.0133  +.000044P,       (18'6) 

where  Z  is  the  span-length  in  thousands 
of  feet.     Hence,  if 

1 


Z=1000',  n=. 123  =  ^2 

orvrw   *    _  ion_  Economic  ratios 

^£v/UU  ,   /& — .  1OU — ._  _    r       /.      •         . 

7.7     of  rise  to  span. 
3000',  n  =  .138  =  ^ 

4000',  n  =.146  =  7^ 

The  above  results  justify  the  value 
of  n  =  \  generally  recommended  for 
spans  of  the  usual  length. 

WORKING  STRESS  IN  THE  CABLE 

In  the  preceding  treatment,  a  value  of 
60,000  Ibs.  per  sq.in.,  was  assumed  for 
the  unit  stress  in  the  cable.  This  con- 
forms to  generally  approved  practice, 


46 


and  affords  a  safety  factor  of  three  (on 
the  elastic  limit). 

The  following  considerations  indicate 
that  the  safety  factor  may  be  judiciously 
reduced  as  the  span  is  increased: 

1.  On  a  longer  span  it  takes  more  time 
for  a  maximum  load  to  come  upon  the 
bridge,  so  that  the  application  of  stress 
is  more  gradual. 

2.  On  a  longer  span  with  the  same 
traffic,   the   combination   of  loads   pro- 
ducing maximum  stress  will  be   much 
rarer  in  occurrence. 

3.  As  the  span  increases,  the  dead- 
load  becomes  a  greater  percentage  of  the 
total  load,  so  that  the   range  of  stress 
variation    in    the    cable    is    diminished. 

4.  The  resistance  of  tension  members 
to    suddenly    applied    stress    increases 
with   their   length,    on   account   of   the 
increase  in  the  resilience  of  the  members. 

5.  It    is   reasonable   to   expect    some 
improvement  in  the  cable  material  before 
the  larger  spans  are  built.     Furthermore, 
the  best  material  can  be  afforded  in  the 
largest  spans. 


47 


For  the  above  reasons  ;  the  unit  cable 
stress  should  be  specified  as  an  increas- 
ing function  of  the  span.  For  this  pur- 
pose, the  following  formula  will  be 
convenient  : 


this  gives 

s0  =  60  ,000  at  1=  1500  } 

s0  =  75,000  at  1  =  3000        .     (19') 

s0  =  86,500  aU  =  4500  j 

and  causes  s0  to  approach  the  limiting 
value  of  s0  =  180.000(=E.L.)  as  I  ap- 
proaches oo  . 

For  substitution  in  the  general  for- 
mulae of  the  preceding  investigation,  it 
will  be  more  convenient  to  replace  (19) 
by  a  linear  equation  which  will  give 
essentially  the  same  values  for  s0  for  all 
practical  values  of  L  Such  an  equation 
is 

s0  =  45,000  +10Z       .     .     .     (20) 

This  gives,  as  before, 

s0  =  60  ,000  at  Z=1500 


SQ  =  75,000  at  1  =  3000  •    *      (20/ 


48 


Economic  Rise-ratio,  Corrected  for 
Variable  s0-  Instead  of  assuming  the 
constant  value  of  s0  =  60,000,  let  the 
value  of  s0  be  specified  by  the  linear 
formula 

so  =  45,000 +10L     .     .     (20) 

Substituting  this  value  in  Eqs.  (18a)  and 
(186)  we  obtain  the  two  formulas 


_  .0093?  +  V.01359  +  .00271+  .0000787*2 
1+0.198Z 

(21a) 

and 

_  .00874? -f  V.Q17Q1  +  .Q033Z+  .000072ft 
1+0.192Z 

(216) 

Case  I.     If  there  are  no  suspenders  in 
the  side-spans,  Eq.  (2 la)  gives  for 

Z  =  0,  (s0  =  45,000),  n= .  116 

Z=1000,  (s0  =  55,000),  n=.  115 

Z  =  2000,  (s0  =  65,000),  n  =  .  113 

Z=3000,  (s0  =  75,000),n=.lll 

Z  =  4000,  (s0  =  85,000),  n=.  110 


49 

Hence,  for  suspension  bridges  of  this 
type,  the  economic  cable-rise  is  about 
one-ninth  of  the  span. 

Case  II.  If  the  side-spans  are  also 
suspended  from  the  cable,  Eq.  (216)  gives 
for 


Z=1000',  (SQ  =  55,000),  n=.  127 

Z  =  2000',  (sQ  =  65,000),  n  =  .  124 

Z  =  3000',  (s0  =  75,000),  n  =  .  122 

Z  =  4000',  (SQ  =  85,000),  n  =  .  120 

Hence,  for  suspension  bridges  of  this 
type,  the  economic  cable-rise  is  about 
one-eighth  of  the  span. 

The  above  rise-ratios  will  be  used  in 
the  following  designs.  The  versed-sine 
(fi)  in  the  side-span  is  fixed  by  the 
relation 

^--frV  (22) 


necessary  for  equal  cable  inclinations  at 
the  towers.  In  the  absence  of  any 
governing  conditions,  the  side-spans  will 


50 


be  assumed  one-half  the  length  of  the 
main  span,  so  that  we  must  have 

/i={  ....     (220 

ART.  5 

MINIMUM  DEPTH  FOR  THE   STIFFENING 
TRUSS 

If  a  simple  truss  of  span  I  is  covered 
with  a  uniform  load  q,  the  deflection 
at  the  mid-point  will  be 

0 QQ/I     7?  T  >         *        *         *         ^     ' 


the  inclination  (or  slope)  at  the  ends  of 
the  span  will  be 

dN      r~2M  16  oP 


the  bending  moment  at  the  mid-point  is 
M=f;  (3) 


51 

and  the  corresponding  chord-stress  is 
Md 


where  d  is  the  depth  of  truss  and  / 
is  its  moment  of  inertia  (assumed 
constant)  . 

Eliminating  M  and  q  from  Eqs.  (1), 
(3)  and  (4),  we  obtain 


(5) 


Eliminating  q  from  Eqs.  (1)  and   (2) 
we  obtain 

dN         N0 


Eliminating  N0  from  Eqs.  (5)  and  (6),  we 
find 

dN_2   si   l_  f7. 

dx     3    Ed' 

In  the  stiffening  truss  hinged  at  the 
towers,  the  maximum  stresses  occur 
with  a  load  extending  over  one-half 
of  the  span.  Each  half  of  the  truss  then 
acts  very  nearly  as  a  simple  beam  carry- 


52 

ing  a  uniform  load  (  =  actual  load  — 
suspender  forces).  We  may  therefore 
apply  the  preceding  formulae,  (1)  to  (7), 
upon  replacing  I  by  the  half  -span  of  the 

suspension  bridge  (=  —  ].     Eq.  (7)  then 

\     ^  / 

becomes 

dN_l£i  I  ,7,x 

dx~3  E'd' 

Hence,    if    the    maximum    allowable 

grade  (-T-)   is  specified,  the  minimum 
\dx  / 

depth  of  truss  will  be  defined  by 


If  5i  =  20,000  (i.e.,  30,000  minus  wind- 
stresses,  secondary  stresses,  column-flex- 
ure stresses,  etc.),  #  =  30,000,000,  and 

-r-  =  1  per  cent  (a  limiting  value  for  rail- 
ctx 

road  bridges),  we  find 

Min.  ~  =—  .  (9) 

1     45 


53 

ART.  6 
ECONOMIC  DEPTH  OF  STIFFENING  TRUSS 

It  can  readily  be  shown  that  the  cost 
of  the  cable  is  unaffected  by  any  change 
in  the  depth  of  the  stiffening  truss, 
within  the  limits  of  practice.  The  effect 
upon  the  weight  of  the  web-members 
is  also  negligible.  We  may  therefore 
define  the  economic  depth  of  stiffening 
truss  as  the  depth  which  will  render  the 
chord-areas  of  the  truss  a  minimum. 

By  Eq.  (5)  of  the  preceding  article 
the  intensity  of  stress  in  the  chords 
of  the  truss  produced  by  a  cable 
deflection  =  Af  is 

ip  j 
8-4.8^.  J/.     .     .    .     (1) 

If  AL  is  the  total  elongation  of  the  cable,, 
then1 


1  Cf  .  Melan,  Theorie  der  eisernen  Bogen-  und 
Hangebrucken  (Leipzig,  1906),  p.  14,  Eq.  (39.) 


54 

For  n=~=—,  tMs  equation  reduces  to 

I     o 

J/=1.62.JL     .     .     .     (20 

The  cable-stretch,  JL,  is  composed  of 
the  elongation  due  to  live-load  plus  the 
temperature  expansion,  or 


where  s0  is  the  total  cable  stress  pro- 
ducible by  the  combined  effect  of  the 
live-load  (p)  and  the  dead-load  (g). 

The  total  length  of  the  cable  is  given 
by1 


cai     (4) 

For  n  =  J  and  nx=^;  this  yields 

L  =  2.Ul.        .     .     .     (40 

1  Cf  .  Melan,   Theorie  der  eisernen  Bogen-  und 
Hdngebriicken  (Leipzig,  1906),  p.  14,  Eq.  (43). 


00 


Substituting  the  values  of  (2'),  (3)  and 
(4')   successively  in   (1),  we  obtain 


If  M  is  the  bending  moment  produced 
by  the  live-load,  and  k  is  the  correspond- 
ing unit  stress,  the  chord-section  will  be 

»•-£  .....  » 

The  value  of  the  moment  may  be  written 
M  =  m.p-P,        .     .     .     (7) 

where  m  is  a  factor  nearly  constant  for 
all  sp&ns 

(  =  ^Q  approximately  l). 

If  §1  is  the  total  allowable  chord-stress, 
deducting  the  stress  (s)  caused  by  the 
deflections,  there  remains, 

k  =  si-s    ....     (8) 

1  Cf.  Burr,  Ancient  and  Modern  Engineering' 
(1903),  p.  175. 


56 


Substituting  the  values  of  (7),  (8)  and 
(5)    successively    in    (6),    there    results 


(9) 


For  a  minimum  chord-area,  the  de- 
nominator of  the  above  expression  must 
be  made  a  maximum.  The  necessary 
condition  is 


Si-32.88/s0 
\ 


9  +  P 
or 

Ec0n°mic      = 


Substituting 

Qnf^-U  26000, 


and  ^^=12000,  Eq.  (10)  becomes 

.    d              791 
Economic  y  = .   (100 

+ 12000 


57 


Assuming  a  cable-stress  increasing  with 
the  span-length  (cf.  Art.  4)  and  taking 

-  from  the  results  of  the  writer's  designs 

P 

we  find,  with  the  aid  of  Eq.  (10'),  for 


Z=  1500,     =1.8,  s0=60;000, 
p 

=2250,     =2.3,     =67,500, 


=3000,     =3.1       =75,000  -JL 

oo 

Mean=-L, 

This  value  is  somewhat  higher  than  the 
average  of  past  practice,  probably  be- 
cause most  designs  have  been  a  com- 
promise between  the  demands  of  economy 
and  those  of  aesthetics.  The  Williams- 
burg  Bridge  is  the  only  long-span  struc- 
ture conforming  to  the  above  economic 
ratio,  but  its  appearance  is  undoubtedly 
marred  by  the  excessive  depth  of  the 
stiffening  truss. 


58 


Eq.  (9)  yields 


T=M>,  or, 

d  . 

*! 

1      16.44  (s 

0—7  —  hUutf) 

=  2.(Econ.y^ 
\             ^/ 

That  is,  the  cost  of  the  stiffening  truss 
approaches  infinity  as  the  depth  departs 
from  the  economic  value  either  toward 
a  value  twice  as  great  or  toward  a  zero 
value.  This  shows  that  the  truss  depth 
is  a  very  important  factor  in  the  economic 
design  of  a  suspension  bridge. 

For  the  purpose  of  this  investigation, 
economy  of  weight  and  cost  is  of  greater 
significance  than  any  aesthetic  con- 
siderations. We  shall  therefore  adhere 
to  the  depth-ratio  derived  above,  even 
at  a  sacrifice  of  appearance. 

It  will  be  noted  that  the  above  value 


of 


— I }  is  but  little  in  excess  of  the 
40. 


59 


minimum  permissible   depth  (  =— /)  as 

\     45  / 

found  in  the  preceding  section. 


BIBLIOGRAPHY     ON     SUSPENSION 
BRIDGES 

Williamsburg,  (N.  Y.)« 

Engineering  Record,  1895  (II,  pp.  127,  142); 

1898  (II,  p.  228);    1902  (I,  p.  148);   1903 

(I,  pp.  80,  482;    II,   pp.  277,   756,    809); 

1908  (I,  p.  658). 
Engineering  News,  1896  (II,  p.  126);    1897 

(II,  p.  173);    1898  (I,  p.  114);    1899  (I,  p. 

330);    1901   (I,  p.  289;    II,  p.  2);    1902 

(I,  p.  182;    II,  pp.  124,  198);    1903  (I,  p. 

81;   II,  p.  535). 
Railroad    Gazette,    1896    (July    31);     1898 

(Feb.  11). 

Iron  Age,  1896  (Sept.  24). 
Zentralblatt    d.    Bauverwaltung,    1896    (p. 

442). 
Zeitschrift    d.    Ver.    deutscher    Ing.,    1904 

(p.  1213). 
Engineering,  1905  (Oct.  27). 

Brooklyn,  (N.  Y.). 

Deutsche    Bauzeitung,    1870,     1873,    1876, 

1878,  1880. 
Journal  of  the  Franklin  Institute,  1873. 


60 


Scientific  American,  1873,  1876,  1877,  1878, 

1882. 
Engineering,   1873,  1876,  1877,  1878,  1879, 

1890. 

Schweiz.  Bauzeitung,  1883. 
Engineer,  1874,  1877,  1881. 
Annales  des  ponts  et  chausse'es,  1874. 
Trans,   of  the  Amer.   Soc.   of  Civ.  Engrs., 

1877. 

Nouv.  ann.  de  la  constr.,  1879,  1880 
Harper's  Magazine,  May,  1883. 
Johnson's  Cyclopaedia  (1896);    "  Bridges." 
Railroad  Gazette,   Nov.  23,   1894;    Dec.  9, 

1898;   Jan.  10,  1902. 
Van  Nost rand's  Science  Series,  No.  32. 
Engineering  News,  1901  (Oct.  10);    1902. 

Manhattan,  (N.  Y.). 

Engineering  Record,  1900  (May  12);    1898 

(Jan.  22);    1904  (July  2,  Dec.  17);    1905 

(July  29,  Nov.  25,  Dec.  2);    1906  (Aug. 

25);    1908  (Nov.  21,  Oct.  31);    1908  (Apr. 

4,  Aug.  8,  Dec.  5);    1909  (Apr.  3,  Oct.  2); 

1909  (July  31). 
Engineering    News,    1905    (Aug.    3);     1909 

(Oct.  14). 
Scientific  American,  1908. 

Niagara. 

Ann.  des  ponts  et  chausse'es,  1877. 
Engineering  (London),  1881. 
Nouv.  ann.  de  la  constr.,  1880. 


61 

Zeitschr.  f.  Bauk.,  1883. 

Railway  Age,  1898  (Dec.  30). 

Engineering  Record,   1897  (Apr.  24),   1899 

(Aug.  26). 
Engineering  News,  1899  (Jan.  12). 

Ohio  R.  (Cincinnati). 

Engineering  Record,  1898  (Sept.  10,  Nov.  26) 

Miampimi  (Mexico). 

Engineering  Record,  1900  (Oct.  20). 
Zeitschr.  f.  Transportw.  u.  Strassenb.,  1902 

(p.  348). 

Elizabeth  (Budapest). 

"Die     Eisenkonstruktion     der     Elisabeth- 

Kettenbriicke  im   Budapest"    (Published 

by  the  Government),  1904. 
Deutsche  Bauzeitung,  1895. 
Schweiz.  Bauzeitung,  1895  (I,  p.  48);    1897 

(I,  p.  148;   II,  p.  168). 
Engineer,   1895   (II,  p.   106);    1904   (I,  pp. 

379,  429,  438,  503,  514,  579,  628). 
Engineering  Record,    1895   (Oct.   5);     1895 

(Aug.  24);    1900  (Nov.  10). 
Oesterr.  Monatschrift  f .  d.  Oeffent.  Bandienst, 

Apr.,  1899. 
Zeitschr.  d.  osterr.  Arch.  u.  Ing.  Ver.,  1904 

(pp.  261,  277). 
Zeitschr.  f.  Transportw.  u.  Strassenb.,  1904 

(p.  366). 

Engineering  News,  1905  (Aug.  24). 
Engineering  Mag.,  1906  (March). 


62 


Freiburg,  (Saane  R.,  Switzerland). 

Chaley,    "Pont    suspendu   sur    la    Saane   & 

Freiburg,"  Paris,  1835. 
Allgemeine  Bauzeitung,  1836. 
Zeitschr.  f.  Bauw.,  1863. 
Nouvelles  annales  de  la  construction,  1881. 
Riese,  "Die  Ingenieurbawerke  der  Schweiz." 

Rochester,  (Ohio  R.). 

Engineering  News,  1897  (I,  p.  194). 
Point  (Pittsburg). 

Engineering  News,  1877. 

Railroad  Gazette,  1878. 

Ann.  des  ponts  et  chausse"es,  1879,  II. 

Deutsche  Bauzeitung,  1879. 

Engineering   Record,    1903    (I,    pp.    2-10); 
1901  (I,  pp.  424,  455);    1905  (I,  p.  517). 

Vernaison  (France). 

G&rie  civil,  1903  (I,  p.  145). 
Engineer  (London),  1903  (p.  62). 
Nouv.  ann.  de  la  constr.,  1903  (p.  162). 
Sci.  Am.  Supp.,  1903  (Oct.  10). 
Engineering  Record,  1904  (Sept.  10). 

E.  Liverpool  (Ohio). 

Engineering  News,  1897  (I,  p.  198). 
Clifton  (Bristol,  Eng.). 

Zeitschr.  d.  osterr  Ing.  u.  Arch.  Ver.,  1863. 

Zeitschr.  d.  Arch.  u.  Ing.  Ver.  zu  Hannover, 
1865. 


63 


Lancz  (Budapest). 

Clark,  "An  Account  of  the  Suspension 
Bridge  across  the  River  Danube,"  Lon- 
don, 1853. 

Morgantown  (Monongahela  R.,  W.  Va.). 

Engineering  News,  1905  (Mar.  9);  1907 
(Apr.  18). 

Menai  (Wales). 

Smiles,  "Lives  of  the  Engineers"  (Telford). 

Villefranche  de  Conflent  (France). 

Engineering  Record,  1905  (I,  p.  171). 

Caperton  (W.  Va.). 

Engineering  Record,  1904  (Aug.  6). 

Moldau  (Prague). 

Kostlin,  "Ueber  die  neue  Moldau-Briicke  in 

Prag,"    in    Zeitschr.    d.    osterr    Arch.    u. 

Ing.  Ver.,  1868. 
Schmitt,    "Der   neue    Kettensteg   iiber   die 

Moldau  in  Prag,"  Prague,  1870. 

Charleston,  (W.  Va.). 

Engineering  News,  1905  (Feb.  2). 
Engineering  Record,  1904  (Dec.   24),  (Dec. 
31). 

Tweed  (Berwick,  Eng.). 
American        Encyclopedia,        "  Suspension 
Bridges." 

Lambeth  (London). 

Heidmann,   "Die  Lainbeth-Brucke  in  Lon- 


64 

don,"  in  Zeitschr.  d.  osterr.  Ing.  u.  Arch. 
Ver.,  1863. 

Conway  (Chester,  Eng.). 

"The  Conway  Suspension  Bridge,"  Engineer, 

1881  (p.  27). 
Engineer,  (London),  1904  (May  20). 

Hudson  R.  (Projects). 

Report  of  Board  of  Engineers,  Washington, 

1894. 

Ann.  des  travaux  publ.,  1890  (p.  175). 
Engineering    News,    1894    (Sept.   13);    1901 

(May  16). 
Engineering  Record,  1894  (II,  pp.  375,  390); 

1895  (I,  p.  275,  II,  p.  20). 
Railroad  Gazette,  1894  (Sept.  14). 
Ge*nie  civil,  1894  (I,  p.  193),  1895  (I,  p.  57). 
Stahl  u.  Eisen,  1896  (p.  174). 
Scientific  American,  1896  (May  2). 
Proc.  of  the  Am.  Soc.  of  Civ.  Eng.,   1896 

(p.  469). 
Trans.  Assn.  of  Civ.  Engs.  of  Cornell  Univ., 

(G.  Lindenthal)  1896. 
Engineering  Magazine,  1898  (Dec.). 
Proc.  N.  Y.  R.  R.  Club,  1901  (Apr.  18). 


65 


CHAPTER  III 
DESIGN  OF  SUSPENSION    BRIDGES 

ART.  7 

PRINCIPAL  DATA  FOR  DESIGN  OF 
SUSPENSION  BRIDGES 

No.  1.     No.  2.      No.3. 

l=Span  =1500,    2250,    3000ft. 

j1=:Side-span=J/2  =  750,    1125,    1500ft. 

/=versed-sine=0.12Z      =   180,      270,      360ft. 
/i= versed-sine  in  side- 
span^/ 4  =     45,     67.5,        90  ft. 
d=depthof  truss=.024Z  =     36,         54,        72  it. 
a=panel     length     (be- 
tween suspenders)      =18.5,    22 . 3,    24 . 8  ft. 
Type:   Stiffening  truss  hinged  at  the  towers. 
Suspension  rods  in  side-spans. 

Loading: 

4  railroad  tracks  at  3000  Ibs.  =  12000  Ibs.  p.l.f. 
2  lines  of  cars  at        1000         =  2000 
40  ft.  of  roadway  at        75         =  3000 
20  ft.  of  roadway  at        50        =   1000 

Total  congested  load  =18000  Ibs.  p.l.f. 

Total  width  of  structure  =  115  ft. +2  cantilevers 
at  10  ft. 

4  Cables,  spaced  37'.5+40'  +  37'.5  c.  to  c. 
4  Trusses,  spaced  37'.5+40'  +  37'.5  c.  to  c. 


66 

ART.  8 
DESIGN  OF  THE  STIFFENING  TRUSS 

By  proper  adjustment  of  the  suspen- 
sion rods  after  the  erection  is  completed, 
all  strain  may  be  taken  out  of  the  stiffen- 
ing truss  before  live-load  is  applied.  The 
dead-load  is  thus  carried  wholly  by  the 
cable  and  may  be  entirely  omitted  from 
consideration  in  designing  the  stiffen- 
ing truss.  The  latter  will  therefore  be 
designed  merely  for  the  uniform  live-load 
of  4500  Ibs.  per  linear  foot,  a  temperature 
variation  of  ±60°F.,and  a  lateral  wind 
pressure  of  30  Ibs.  per  square  foot. 

The  formulae  used  will  be  those  based 
on  the  Theorem  of  Least  Work,  as  de- 
veloped by  J.  Melan  in  his  "Theorie 
der  eisernen  Bogenbriicken  und  Hange- 
briicken."  l  This  theory  has  been  found 

1  Handbuch  der  Ingenieur  -  Wissenschaften 
(Leipzig,  1906),  II.  Band.  V.  Abteilung.  XII. 
Kapitel,  pp.  17-50.  Cf.  Miiller-Breslau,  "The- 
orie  der  durch  einen  Balken  versteiften  Kette." 
Zeitschr.  d.  Arch,  und  Ing.  Ver.  zu  Hannover, 
1881,  p.  57.  Am  Ende,  "Suspension  Bridges 
with  Stiffening  Girders,"  Proc.  of  the  Inst.  of 


67 

by  the  writer  to  give  results  essentially 
the  same  as  those  yielded  by  formulae 
established  in  a  different  manner  by 
M.  Maurice  Levy  in  his  "  Calcul  des  ponts 
suspendus  rigides/' l  and  by  those  of  C. 
Schwend  in  his  treatise  on  suspension 
bridges.2 

The  above  theories  involve  the  follow- 
ing common  assumptions:3 

1.  The    cable    is    supposed    perfectly 
flexible,  freely  assuming  the  form  of  the 
equilibrium   polygon    of    the    suspender 
forces. 

2.  The   truss   is   considered   a   beam, 
initially  straight  and  horizontal,  of  con- 
stant moment  of  inertia  and  tied  to  the 
cable  throughout  its  length. 

C.E.,  1899,  p.  306;  and  A.  J.  Dubois,  "The 
Stresses  in  Framed  Structures,"  New  York, 
1896. 

1  Annales  des  Ponts  et  Chaussees,  1886,  II., 
p.  179,  et  seq. 

2  Schwend,  Ueber  Berechnung  und  Konstruktion 
von  Hangebrucken  unter  Anwendung  von  Stahl- 
draht-Kabeln  und  Versteifungsbalken  (Leipzig, 
1887). 

3Cf.  M.  T.  Godard,  Annales  des  Ponts  et 
Chaussees,  1894,  II.,  and  Melan,  p.  17. 


68 


3.  The  dead-load  of  truss  and  cable  is 
assumed  uniform  per  linear  unit,  so  that 
the  initial  curve  of  the  cable  is  a  parabola. 

4.  The  form  and  ordinates  of  the  cable 
curve  are  assumed  to  remain  unaltered 
upon  application  of  loading. 

All  of  these  assumptions,  with  the  ex- 
ception of  the  last,  are  ver,y  near  the  actual 
conditions  even  in  the  case  of  flexible 
trusses.  The  last  assumption  is  admissi- 
ble only  with  trusses  of  sufficient  rigidity, 
and  its  exclusion  results  in  the  "  Genauere 
Theorie,"  developed  by  Melan.1  For  the 
purposes  of  this  investigation,  the  Least 
Work  Theory  will  be  deemed  sufficiently 
accurate,  its  variations  from  the  Exact 
Theory  being  negligible  and  on  the  side 
of  safety. 

Live-load  Stresses.  The  bending  mo- 
ment at  any  section  (x)  of  the  main  span 
(7),  produced  by  a  load  (p)  covering  the 
entire  length  of  the  bridge  ,  is 


1  Melan,  p.  50,  et  seq. 


69 
where 


The  results  of  preliminary  estimates  of 
truss  and  cable  gave 

for  I  =    1500     2250     3000 

_/_        A        _i        JL 
A0f2        62        75        94* 

With  these  values,  assuming  /=/i,  we 
obtain 

N  -     1.82,    1.80,    1.78. 
and 

M=0.0322,    0.0278,    0.0230ps(Z-x). 

The  same  relation  obtains  for  the  side 
spans,  upon  substituting  l\  for  I.  The 
above  figures  may  be  interpreted  as  indi- 
cating that  the  truss  in  each  case  serves 
to  carry 

6.44%         5.56%         4.60% 

of  the  total  load,  the  remainder  being 
carried  by  the  cable. 


70 

The  position  (£  =  n-l)  of  a  concentra- 
tion producing  zero  bending  moment  at 
any  section  (x)  of  the  truss  is  called  the 
critical  point  for  that  section  and  is  given 

by 


*  y 

=  .218,      .216,      .214-.        (3) 

y 

The  roots  of  this  equation  for  different 
values  of  x  are  most  easily  obtained  from 
a  graph  of  the  function 

which,  once  plotted,  can  be  used  for  all 
suspension  bridge  designs. 

For  the  greatest  negative  moment  at 
any  section  (x)  of  the  main  span,  the 
load  should  cover  both  side  spans  and 
the  portion  (I—?)  of  the  main  span  be- 
tween the  farther  end  and  the  critical 
point.  The  resulting  bending  moment  is 
„  2px(l  -x) 


K-F-fl   <4> 


71 

A  graph  of  the  function  f(ri)  = 
(2—  ft—  4n2-f  3n3)  was  used  by  the  writer 
to  simplify  the  labor  involved  in  the 
repeated  application  of  the  above  formula. 

For  the  greatest  positive  moment  at 
any  section  of  the  main  span,  that  span 
is  loaded  from  x=0  to  x=£,  giving 

Mmax  =  Mtot  -  Mmin  .         .     (5) 

There  are  no  critical  points  in  the  side 
spans.  For  the  greatest  negative  mo- 
ment at  any  section  (x)  in  one  of  the  side 
spans,  load  the  other  two  spans,  giving 


-x) 

•'•"•mm  r  TVT 


which  reduces  to 

Mmin=  -.455,     -.459,     -ASZpx^  -x). 

Loading  the  span  itself  produces  the 
greatest  positive  moments: 

-Mrnax  =  Mioi  —M  min  = 

.487,  .487,  ASSpx^-x). 


72 


With  all  spans  completely  loaded,  the 
shear  at  any  section  (x)  of  the  main  span 
will  be 


(7) 

In  the  designs  at  hand,  this  reduces  to 
Stot=.0644,    .0556,     . 


the  coefficient  in  each  case  representing 
the  fraction  of  the  total  load  carried  by 
the  truss.  The  same  relations  apply  to 
the  side  spans  upon  replacing  I  by  Zi  . 

The  critical  point  (£  =  n-Z)  for  zero 
shear  at  any  section  (x)  of  the  truss  is 
given  by 


This  formula  is  solved  by  the  same 
graph  as  that  used  for  Eq.  (3).  For 
maximum  shear  at  any  section  of  the 
truss,  the  load  should  extend  from  #  =  0 
to  the  given  section,  and  from  the  critical 


73 


point  to  the  farther  end  of  the  span. 
The  shear  will  then  be 


There  will  be  no  critical  point  for  any 
section  where 


x>      l  -  j   =  .272^,      .275Z,      .278Z. 

For  all  such  sections,  n=  1,  and  the  last 
term  in  the  equation  for  /Smax  vanishes. 

There  are  no  critical  points  in  the  side 
spans,  the  maximum  shear  at  any  section 
being  simply 


-IK)  '41! 


74 
A  graph  of  the  function 


serves    to    simplify    the    application    of 
Eqs.  (9)  and  (10). 

The  stresses  in  the  diagonal  web  mem- 
bers are  obtained  by  dividing  the  shear 
at  any  section  by  the  number  of  web 
members  cut  by  that  section,  and  multi- 
plying the  quotient  by  the  secant  of  their 
inclination  to  the  vertical. 

Temperature  Stresses.  The  cable-ten- 
sion produced  by  a  rise  in  temperature 
(t)  is  given  by 

ZEIwtL 

Ht==  ~ 


For  an  extreme  variation  of  t=  ±  60°  F., 
Ewt=l  1,720.  Taking  the  value  of  / 
from  preliminary  estimates,  Eq.  (1) 
yielded 

#,  =  260,     420,     560  kilo-pounds. 

The  resulting  bending  moment  at  any 
section  of  the  truss  is  given  by 

Mt  =  HtY  .  .     (2) 


75 

and  the  transverse  shear  by 

S,  =  #rtanr,      .     .     (3) 

where  T  is  the  inclination  of  the  cable  at 
the  given  section. 

Wind  Stresses.  Let  p—  the  total  hori- 
zontal wind-load  per  linear  foot.  The 
resulting  lateral  deflection  (h)  causes  a 
displacement  of  the  plane  of  the  cable 
and  suspenders  from  the  vertical ,  thereby 
giving  rise  to  a  force  of  restitution  (r) 
equal  to  the  horizontal  component  of 
the  suspender  tensions.  If  v  is  the  mean 
vertical  distance  of  the  truss  and  live 
load  below  the  cable  chord,  then  the 
reaction  component  of  the  displaced 
weight  (W)  will  be 

r=\-W (1) 

Considering  the  truss  as  a  beam  acted 
on  by  a  uniform  horizontal  load  (p— r), 
we  have 


76 

From  (1)  and  (2) ,  there  results 
E.JLA 

r= — ~w — = — T  'P-       '     (3) 

1+T*384*^Z 
In  the  designs  at  hand,  Eq.  (3)  yields 

r/P  =     19%;      45%;      57% 
in  the  main  spans,  and 

r/p  =  3.5%;     9.3%;     20.3% 

in  the  side-spans. 

The  specified  wind-load  (p)  consists 
of  a  pressure  of  30  Ibs.  per  square  foot 
acting  on  the  exposed  surface  of  one 
truss  and  on  half  that  of  the  remaining 
trusses,  also  on  a  train  of  cars  14  ft.  high. 
On  the  round  surface  of  the  cables,  only 
one-half  of  the  above  pressure  is  con- 
sidered effective.  The  total  wind  pres- 
sure in  our  designs  is  thus  found  to  be 

p=  1220;     1400;     1545  Ibs.  p.l.f. 

and  the  effective  horizontal  pressure  will 
be 

p-r=988;       772;       671  Ibs.  p.l.f. 


77 

in  the  main  spans,  and 

p  -r=  1177;       1270;       1231  Ibs.  p.l.f. 

in  the  side-spans. 

The   resulting  lateral   deflections,   by 
Eq.  (2),  will  then  be 

&=18i";      481";     61" 
at  the  center  of  the  main  span,  and 


at  the  center  of  the  side  -span. 

Each  of  the  above  pressures  (p—r) 
must  be  resolved  into  two  parts  acting  in 
the  planes  of  the  upper  and  lower  lateral 
systems  respectively.  On  account  of  the 
wind  pressure  on  the  floor  and  train,  the 
lower  chords  get  the  major  share  of  the 
wind-load,  amounting,  in  the  present 
designs,  to  about  63%  of  the  total 
pressure. 

The  system  of  bracing  adopted  is  simi- 
lar to  that  used  on  the  Manhattan  Bridge. 
The  upper  lateral  bracing  consists  of  diag- 
onals and  struts  connecting  the  inside  to 
the  outside  trusses.  There  is  no  bracing 
over  the  roadway  or  sidewalks.  The 


78 


upper  lateral  system  is  therefore  com- 
posed of  two  independent  horizontal 
trussses,  37.5  ft.  deep,  so  that  the  chord- 
stresses  due  to  the  wind  moments  will 
equal  Af^-r-75. 

The  lower  lateral  system  consists  of 
the  four  lower  chords  tied  together  by 
the  floor  beams  and  special  diagonal 
braces  extending  across  the  entire  floor. 
Assuming  the  wind-stresses  in  the  chords 
to  vary  as  their  respective  distances  (20  ft. 
and  57.5  ft.)  from  the  neutral  axis,  the 
stress  in  the  outside  lower  chords  will 
equal  M^-f-129. 

It  is  thus  found  that  the  wind-stresses 
in  the  upper  and  lower  chords  are  almost 
equal,  so  that  the  same  sections  may  be 
used  for  both. 

In  designing  the  members  of  the 
lateral  systems,  the  wind  pressure  is 
considered  as  a  moving  load.  The  max- 
imum shear  at  any  section  (x)  is  given  by 


and  the  resulting  stresses  are  obtained 


79 

by  dividing  this  shear  by  the  number  of 
laterals  cut  by  the  section  and  multiply- 
ing the  quotient  by  the  secant  of  their 
inclination. 

Working  Stresses.  The  chords  of  the 
stiffening  truss  are  made  of  nickel  steel 
and  are  designed  for  working  stresses  of 
30,000  Ibs.  per  square  inch  in  tension  and 

/  P     \ . 

for  30 ,000 -*-  (!+•          Jin  compression. 

The  web  members,  bracing  and  con- 
nection details  are  of  structural  steel  and 
are  designed  for  working  stresses  of 
20,000  Ibs.  per  square  inch  in  tension  and 

/  I2    \ 

for  20 ,000 -f-  (1+  Jin  compression. 

Computations.  The  limitation  of  space 
renders  it  impracticable  to  reproduce 
here  the  detailed  computations  of  the 
stresses  and  weights  of  members.  For 
the  same  reason,  the  design  of  the  floor 
system  will  not  be  given  here.  The  final 
weights,  however,  are  tabulated  in  the 
following  article: 


80 

ART.  9 
DESIGN  OF  SUSPENDERS 

The  load  carried  by  the  suspenders 
consists  of  the  following  items: 


Truss  and  bracing 
Floor 
Suspenders 

Total  Dead-load 
Live-load 

Total  load  p.Lf  . 
(-ft) 

Total  load  per 
suspender 

S.  B.         S.  B.          S.  B. 
No.  1.         No.  2.         No.  3. 

2,624       4,015       5,786  Ibs. 
3,712       3,800       3,812 
126          207          320 

6,462       8,022       9,918 
4,500       4,500       4,500 

10,962     12,522     14,418  Ibs. 

202,800  279,800  358,000  Ibs. 

With  a  specified  working  stress  of  30,000 
Ibs.  per  square  inch,  the  required  sec- 
tions for  the  suspenders  will  be: 


6.8        9.3    11.9  sq.  in. 
Their  average  length 

(=*/+*=  96        144      192ft. 

Hence,    their    mean 

weight=  126        207      320 


Ibs.  p.l.f .  of  truss, 
as  assumed  above. 


81 

ART.  10 
DESIGN  OF  CABLES 


Preliminary  Estimate.  For  an  accu- 
rate design  of  the  cable  its  weight  must  be 
known  in  advance.  For  this  purpose, 
use  is  made  of  Eq.  (5)  of  Art.  4,  viz.: 


go  =01  • 


'- 

n 


With    /c=  -  ,    and    n=-=0.12,    the 
136000  I 

above  reduces  to 

.000068Z 

flfo""9fll-.00006Sf 

or,  for 

Z=1500,     2250,     3000, 
0o  =  .  1140!,  .1810!,  .25701. 

Taking  the  values  of  the  total  suspended 
load  (0i)  from  the  preceding  article,  we 
find  the  weight  of  the  cable  to  be 

go=1250,  2270,  3710  Ibs.  p.l.f. 


82 


After  a  first  design  these  values  were 
slightly  altered  to  those  given  below 
for  the  final  computation. 

Final  Computation.  The  total  load 
carried  by  the  cables  consists  of  the 
following  items : 

s.  B.         s.  B.       s.  B. 

No.  1.  No.  2.  No.  3. 
Dead-load    on    sus- 
penders (as  above)         6,462  8,022  9,918 
Weight  of  cable                  1,286  2,160  3,720 


Total  dead-load  (=0)        7,748     10,182     13,638 
Live-load  (=p)  4,500       4,500       4,500 

Total  load  p.Lt.(=g+p)  12,248     14,682     18,138 

For  a  live-load  (p)  covering  the  main 
span,  the  horizontal  component  of  the 
cable  tension  will  be 


In  the  designs  at  hand,  this  gives 
#=.9170;     .9250;     .9365  pi. 

For  a  live-load  (p)  covering  one  of  the 
side-spans,  the  cable  tension  is  given  by 

l   fl    I    h2    l 


83 

In  the  present  designs  this  gives 
#=.0572;     .0578;     .0585  pZi. 

Combining  the  above  values,  we  find 
the  cable  tension  for  a  uniform  live-load 
(p)  covering  all  the  spans  to  be 

Hp  =.9742;     .9840;    .9950  pZ. 

As  the  cable  sustains  the  entire  dead- 
load  (g)  without  any  relief  from  the 
stiffening  truss,  the  corresponding  hor- 
izontal tension  will  be 

_gl2_gh2 

g~8f~8fr'    '    '    * 
or,  in  the  designs  at  hand, 

#0=1.04170*. 

Substituting  the  values  of  (g)  and  (p) 
in  the  above  expressions  for  H,  we 
obtain 

#0  =  12,100,000,  23,880,000,  42,600,000  Ibs. 
HP=  6,135,000,  9,960,000,  13,440,000  Ibs. 

As  previously  given  (Art.  8),  the  cable 
tension  producible  by  a  fall  of  tem- 
perature is 

Ht=      260,000,        420,000,       560,000  Ibs. 


84 

Hence, 

Total  H=  18,495,000,  34,260,000,  56,600,000  Ibs. 

Multiplying  this  value  by  the  secant  of 
the  inclination  of  the  cable  at  the  towers, 
(sec.  =  1.109),  we  find  the  maximum 
cable  tension  to  be 

Tmax  =  20,510,000  Ibs.,    38.000,000  Ibs.,    62,770,000  Ibs. 

With  the  specified  unit  stress  of  60,000 
Ibs.  per  square  inch,  the  required  cable 
section  (per  truss)  will  be 

A0  =  342,     633,     1046  sq.in. 
This  section  will  be  provided  as  follows: 

S.  B.  No.  1.      One  cable  of  37  strands, 

each  containing  319  wires  of  0.192  in. 

diam.    Diam.  =  23f  in.      Total  area  = 

342  sq.in. 
S.  B.  No.  2.  Two  cables  of  37  strands, 

each  containing  296  wires  of  0.192  in. 

diam.     Diam.  =  22-|  in.     Total  area  = 

634  sq.in. 
S.  B.  No.  3.  Three  cables  of  37  strands, 

each  containing  326  wires  of  0.192  in. 

diam.     Diam.  =  24  in.      Total  area  = 

1047  sq.in. 


85 


Each  cable  will  be  wrapped  with  a 
single  layer  of  No.  10  (B.  W.  G.)  iron 
wire. 

Allowing  for  catenary,  cable  wrapping, 
etc.,  the  mean  weight  of  the  cables  will 
be 


2160,    3720  Ibs.  pj.f. 
as  assumed  above. 

ART.  11 
DESIGN  OF  TOWERS 

Each  tower  will  consist  of  four  box- 
columns,  one  for  each  cable  system, 
rigidly  tied  together  by  transverse  brac- 
ing in  a  vertical  plane.  Comparative 
designs  by  the  writer  indicated  a  small 
economy  of  material  in  favor  of  pin- 
bearing  columns,  but  this  saving  is 
more  than  outweighed  by  the  more 
expensive  construction,  greater  dif- 
ficulty of  erection,  uncertainty  of 
action  and  aesthetic  inferiority  due  to 
the  impression  of  instability.  The  more 


86 


usual  design,  namely  with  the  columns 
rigidly  fixed  at  the  base,  will  therefore 
be  followed. 

Assuming  the  required  clearance  of 
the  truss  above  M.  H.  W.  to  be  135,  160 
and  185  ft.  for  the  respective  bridges, 
and  assuming  the  top  of  the  masonry 
piers  to  be  30  ft.  above  M.  H.  W.,  the 
total  height  of  the  steel  towers  will  be: 
for 

S.  B.  No.  1,  180+36  +  135-30  =  321  ft. 
S.  B.  No.  2,  270  +  54  +  160-30  =  454  ft. 
S.  B.  No.  3,  360  +  72  +  185-30  =  587  ft. 

Deducting  the  height  of  the  pedestal 
castings,  the  effective  height  of  the 
towers  will  be 

A  =  316;  448;  580ft.; 

and  the  height  up  to  the  stiffening  truss 
will  be 

Ai  =  100;  124;  148ft. 

The  maximum  fiber  stress  in  the  tower 
columns  will  occur  when  the  live-load 
covers  the  main  span  and  the  farther 


87 


side-span  at  maximum  temperature. 
Under  this  condition  of  loading,  the  top 
of  the  tower  will  be  deflected  toward 
the  main  span  as  a  result  of  the  following 
deformations : 

1.  The    upward     deflection     (J/\)    at 
the   center  of    the   unloaded   side-span. 

2.  The  elongation  of  the  cable  between 
the  anchorage  and  the  tower  due  to  the 
elastic  strain  produced  by  the  applied 
loads. 

3.  The   elongation   of   the    cable   due 
to  thermal  expansion. 

These  deformations  are  computed  as 
follows : 

(1)  The  upward  deflection  (J/i)  is 
found  by  considering  the  side-span  as  a 
simple  beam  subjected  to  a  downward 
loading  equal  to  the  suspended  dead-load 
(p)  and  an  upward  loading  equal  to 

/  P\ 

the  suspender  tensions    It  =  H -*-  —  J .     If 

Pi(f=£— P)  is  the  resultant  of  these 
loadings,  the  central  deflection  will  be 

jA-JLEilli  m 

4/1  "384    El      '     '    '     W 


88 

For  the  spans  under  investigation,  this 
gives 

J/i  =  2.630;  3.760;  4.885  ft. 

(2)  The  elastic  elongation  of  the  cable 
in  the  side-  span  is  given  by 


H    Cds* 

l    ET0-Jdtf 


which  reduces  to 

JL1==  1.915;  2.875;  3.860ft. 

(3)  The  temperature  expansion  of  the 
cable  in  the  side  -span  is  given  by 

-T- 
ax 

(3) 


t  I  -T- 
J  ax 


which   reduces  to 

JLi  =  0.390;  0.585;  0.780ft. 

The  length  of  the  cable  in  the  side-span 
is  given  very  closely  by 

)      (4) 


89 

from  which  we  find 
dLi 


77—  —  ^  A  ~r  ^  y~2  n~  ^  van.   ULI  j  —  1 . 125,        (5) 

and 


The  deflection  of  the  top  of  the  tower  is 
then  given  by 


,_ 


Substituting  the  values  from  (1),  (2),  (3), 
(5)  and  (6)  in  (7),  we  obtain  the  max- 
imum tower  deflection, 

?/o  =  2.798;      4.150;     5.515ft. 

Considering  this  deflection  as  pro- 
duced by  an  unbalanced  horizontal 
force  P  applied  at  the  top  of  the  tower, 
this  force  may  be  calculated  if  the 
sectional  dimensions  of  the  tower  are 
known.  As  these  are  not  known  in 
advance,  the  following  procedure  is 
adopted  : 


90 


Assume  the  moment  of  inertia  of  the 
section  of  the  tower  to  have  a  maximum 
value  (/o)  at  the  base  and  to  diminish 
regularly  toward  the  top  according  to 
some  appropriate  law.  A  study  of 
actual  designs  indicates  the  applicability 
of  the  law  of  variation  represented  by 
the  empirical  formula 

7  =  /o(l-vV/0,        .     .     (8) 

where  x  is  the  distance  of  any  section 
above  the  base.  Substituting  this  rela- 
tion in  the  differential  equation  of  the 
elastic  curve  of  the  cantilever 


and  integrating,  there  results 

P     30^7o  /m 

P  =  23^°'     '     •     '     (9) 

In  the  designs  at  hand,  this  reduces  to 
P  =  3.47070;     1.736/0;     1.094/0. 

The  other  loads  acting  on  the  tower 
are  the  vertical  reaction  (F  =  2#-tan  a) 


91 


at  the  saddles,  and  the  end-shears  (Vi) 
at  the  point  of  suspension  of  the  stiffen- 
ing truss.  In  the  designs  at  hand,  for 
the  condition  of  loading  under  considera- 
tion, we  find 

7=  17,150,000;  30,700,000;  52,100,000  Ibs. 
F!=-  1,037,000;  -1,852,000;  -2,640,000  Ibs. 

At  any  section  (x)  of  the  tower,  the 
horizontal  deflection  (y)  from  the  initial 
vertical  position  of  the  axis  is  given  with 
sufficient  accuracy  by  the  equation  for 
the  elastic  curve  of  the  cantilever: 


This  gives,  for  x  =  hi, 

?/i  =  0.376,    0.436,    0.492ft. 

The    maximum    fiber    stress    at    any 
section  of  the  tower  will  be 

=  7     M-d 
where 


92 

The  moment  of  inertia  for  the  form 
of  section  used  here  is  given  approx- 
imately by 

/  =  0.50A.d2.    .     .     .     (13) 

Substituting  (12)  and  (13)  in  (11),  and 
applying  the  resulting  equation  to  the 
base  of  the  tower,  we  find 

/P\    „     2Vyo2Viyi 

s==  IT  l*™o+"ji-jH  —  T~T 
\/o/  Aodo    ^Mo 

Using  an  allowable  fiber  stress  of 
s  =  24,000  Ibs.  per  square  inch,  and 
substituting  the  numerical  values  of 
P//o,  V,  Fi,  h,  7/0,  and  yi,  as  given 
above,  there  results  the  following 
relation  : 

S.  B.  No.  1: 
24,000=  1096d0+  960070+16113000 


S.  B.  No.  2: 
24,000= 

S.  B.  No.  3: 

o^  AAA   aAvj  ,  800000000  ,  49460000 
24,000=  6474+  -  -r-j  -  +  -  -A  -  . 

AQ 


93 

This  relation  is  satisfied  by  the  follow- 
ing values: 

S.  B.  No.  1:  ^o  =  3240  sq.in., 

do  =  15  ft.;  /.  70  =365,000  in 2  ft.2 
S.  B.  No.  2:  ^o-4260  sq.in., 

d0=  17  ft.;  /.  /o  =625,000  in.2  ft.2 
S.  B.  No.  3:  A0  =  7200  sq.in., 

do  =  20  ft.;  .-.  70=  1,440 ,000  in.2  ft2 

The  horizontal  force  P  is  now  deter- 
mined from  Eq.  (9)  as 

P=694,000;  1,085,000;  1,575,000  Ibs. 

All  the  remaining  sections  of  the  tower 
may  now  be  proportioned,  using  Eq.  (8) 
as  a  guide  and  checking  the  maximum 
fiber  stress  by  Eqs.  (11)  and  (12).  The 
mean  section  of  the  tower  is  thus  found 
to  be 

Mean  A  =  2210;  3240;  5550  sq.in., 

and  the  total  weight,  including  connec- 
tion details  and  bracing  (about  100 
per  cent) ,  is  found  to  be 

Weight  =  4,465,000;  9,720,000 ;  22,406,000 
Ibs.  per  column.     (Structural  steel.) 


94 


Pedestals.  The  pressure  at  the  foot 
of  each  tower  column  is  a  maximum  when 
the  live-load  extends  over  all  the  spans, 
&nd  is  then  made  up  of  the  following 
items : 


Max.  Cable  Reac- 


S.  B.  No.  1.      S.  B.  No.  2.   S.  B.  No.  3. 


tion  (V) 
Max.  Truss  Reac- 
tion (Vi) 
Wt.  of  Tower 
Wt.  of  Pedestal 

17,500,000 

326,000 
4,465,000 
420,000 

32,500,000 

422,000 
9,720,000 
810,000 

53,830,000 

466,000 
22,406,000 
1,200,000 

Total  load  (Ibs.)  22,711,000       42,452,000       77,902,000 

Bearing  area  re- 
quired at  15 
tons  per  sq.  ft.  757  1448  2597 

In  order  to  evenly  distribute  the  above 
loads  over  the  requisite  area  of  masonry, 
the  tower  legs  will  rest  on  pedestals  of 
cast  steel  (annealed)  having  the  follow- 
ing dimensions: 


S.B.No.l. 

Top  of  casting 10  X  30 

Bottom  of  casting    20X40 

Height 5  ft. 

Weight  of  casting 

(Ibs.) 420,000 


S.B.No.2. 

18X34 

30X48 

6ft. 


S.B.No.3. 
24X40 

36X72 
7ft. 


810,000    1,200,000 


95 

ART.  12 
DESIGN  OF  MASONRY  PIERS 

The  steel  castings  at  the  bases  of  the 
tower  columns  are  anchored  on  pedestal 
blocks  of  selected  granite.  The  top 
of  the  pier  is  made  just  large  enough 
to  hold  these  pedestals,  except  where  a 
larger  section  is  required  to  reduce  the 
pressure  in  the  masonry  to  12  tons  per 
square  foot.  The  pier  is  built  of  1 : 2^ : 5 
concrete  with  limestone  (ashlar)  facing. 
The  upper  pier,  above  the  starling,  is 
given  the  section  of  a  rectangle  with 
semicircular  ends  and  has  a  batter 
of  1 : 20  on  sides  and  ends.  In  the  lower 
pier,  the  sides  (batter  1:20)  are  con- 
tinued at  each  end  in  two  circular  arcs 
to  form  a  cutwater  (batter  3 : 20) . 

Below  the  masonry  is  a  rectangular 
cribwork,  used  as  a  coffer-dam  during 
construction.  It  is  built  of  12X12  in. 
timber,  and  is  filled  with  concrete  as 


96 


the  sinking  progresses.  It  rests  directly 
on  the  pneumatic  caisson  which  has  a 
steel  working  chamber  7  ft.  high,  and  a 
reinforced-concrete  roof  3  ft.  thick. 
After  reaching  rock,  the  caisson  and 
shafts  are  carefully  filled  with  1:2:4 
Portland  cement  concrete. 

Since  the  economic  depth  of  founda- 
tions increases  with  the  length  of  span, 
it  will  be  assumed  that  the  pier-depths 
for  the  bridges  under  design  are  somewhat 
greater  for  the  longer  spans.  The  fol- 
lowing are  the  principal  elevations  as- 
sumed : 


S.  B.  S.  B.  S.  B. 

No.  1.  No.  2.  No.  3. 

Top  of  pier 30  30  30 

Starling 5  5  5 

Mean  high  water  (  =  datum)  000 

Base  of  pier=topof  cribwork  —15  —15  —15 

River  bottom -20  -25  -30 

Base  of  cribwork=top  of 

caisson -80  -90  -100 

Cutting-edge  of  caisson  = 

surface  of  rock -90  -100  -110 


The  principal  sectional  dimensions 
of  the  piers,  determined  as  outlined 
above,  are  as  follows: 


97 


S.  B.             S.  B.  S.  B. 

No.  1.  No.  2.  No.  3. 

Top  of  pier 177X42  195X50  225X74 

Base  of  upper  pier.  179X44  197X52  227X76 

Top  of  lower  pier .  200  X  44  222  X  52  259  X  76 

Base  of  pier 206  X  46  228  X  54  265  X  78 

Cribwork 212X52  234X60  271X82 

Caisson 212X52  234X60  271X82 


A  complete  design  and  estimate  of  the 
piers  yielded  the  following  quantities 
of  material  required: 

S.B.No.l.    S.B.No.2.     S.  B.  No.  3. 


12,890 


15,490 
37,400 


Pier  masonry 

Concrete  filling  in 

cribwork ..  .  .       25,300 

Concrete  filling  in 

caisson 4,080 

Timber  in  cribwork  620 

Steel  in  caisson  and 

shafts 1,150,000  2,320,000    2,650,000  Ibs. 

Earth  excavation. .      28,600        39,000         65,000  cu.yds 


5,200 
790 


26,300  cu.yds. 
67,800   " 

8,230   " 

i  n»nJM-ft- 
lt08()(B.M. 


ART.  13 
DESIGN  OF  ANCHORAGES 

The  anchorage,  as  a  mass,  is  required 
to  offer  sufficient  frictional  resistance  to 
sliding  to  resist  the  tension  of  the  cable. 
Dividing  the  maximum  horizontal  tension 
(H)  by  the  coefficient  of  friction  (/*=0.6), 


98 


the  quotient  will  be  the  necessary  weight 
of  anchorage  masonry.  Introducing  a 
factor  of  safety  of  2,  the  masonry  re- 
quired for  the  anchorage  is  thus  found 
to  be 

63,500;       109,000;       183,200  cu.yds. 

This  will  be  built  of  concrete  with  lime- 
stone facing  as  in  the  case  of  the  piers. 

Enclosed  in  the  base  of  the  anchorage 
are  heavy  box  girders  to  which  the 
cables  are  anchored  by  means  of  chains 
of  eye-bars.  -The  total  amount  of  steel 
work  in  each  anchorage  is  found  to  be 

1,037,500;       2,472,500;       4,090,000  Ibs. 

The  anchorage  will  be  supported  on  a 
concrete  foundation  resting  on  bearing 
piles  if  necessary.  The  volume  of  mate- 
rial in  this  foundation  is  found  to  be 

5,290;       10,400;       16,650  cu.yds. 


99 

ART.  14 
ESTIMATE  OF  COST 

In  order  to  establish  an  equitable 
schedule  of  unit  prices  for  the  two  types 
of  bridges,  a  critical  study  was  made  of 
the  different  bids  received  by  New  York 
City  for  the  Williamsburg,  Manhattan 
and  Queensboro  Bridges.  These  struc- 
tures were  selected  as  combining  the 
qualifications  of  recentness  of  date  with 
similarity  of  construction  and  magnitude 
to  the  designs  under  investigation.  The 
prices  of  the  successful  bidders  were 
adopted  except  where  they  differed  so 
widely  from  the  following  bids  as  to 
indicate  their  having  been  unbalanced 
for  some  special  reason.  The  unit  prices 
determined  by  this  comparison  are  in- 
corporated in  the  following  estimates  of 
cost. 


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106 


CHAPTER  IV 

CONCLUSIONS  FOR  SUSPENSION 
BRIDGES 

ART.  15 

EMPIRIC     FORMULAE    FOR   WEIGHTS    OF 
SUSPENSION  BRIDGES 

FROM  the  results  of  the  preceding 
designs,  we  may  construct  semi-empirical 
formulae  for  the  weights  of  the  different 
parts  of  a  suspension  bridge.  Such 
formulae  will  be  useful  in  preparing 
estimates  for  other  spans  and  loadings; 
also  in  drawing  general  conclusions  as 
to  maximum  and  limiting  spans. 

Let  the  weights  (per  linear  foot)  of 
live-load,  cable,  suspenders,  truss  (in- 
cluding bracing)  and  floor  be  represented 
by  L,  C,  S,  T  and  F,  respectively.  The 
weight  of  the  cable  is  evidently  pro- 
portional to  the  total  load  it  sustains 
and  to  the  length  of  span,  provided  the 


107 

rise-ratio  remains  unchanged.  The 
weight  of  the  suspenders  is  likewise 
proportional  to  the  load  they  carry  and 
to  the  span,  as  a  longer  span  requires 
a  proportionally  greater  average  length 
of  suspenders.  The  weight  of  the  truss 
may  be  considered  in  two  parts:  the 
larger  portion  provides  for  the  live-load 
and  is  proportional  to  that  load  and  to 
the  span  length,  if  the  depth  ratio 
remains  constant;  the  other  part  of  the 
truss-weight  represents  the  contribu- 
tion of  the  wind-stresses  and  will  vary 
with  the  square  of  the  span  if  the  width 
of  bridge  remains  constant.  The  weight 
of  the  floor  system  is  evidently  propor- 
tional to  the  assumed  live-load,  and  is 
practically  independent  of  the  length  of 
span.  Introducing  the  necessary  co- 
efficients of  proportionality,  the  above 
relations  may  be  formulated  as  follows: 


108 

Substituting  the  values  of  weights 
and  spans  from  the  preceding  designs, 
the  spans  being  measured  in  units  of 
1000  ft.,  the  above  relations  yield  the 
following  values  for  the  undetermined 
coefficients. 


S.  B.  No.  1. 

S.  B.  No.  2. 

S.  B.  No.  3. 

Mean. 

a=   .070 

.066 

.068 

.068 

b=   .0077 

.0073 

.0074 

.0075 

c=   .35 

.34 

.36 

.35 

d=  105 

105 

105 

105 

e=   .83 

.84 

.85 

.84 

The  uniformity  in  the  above  coefficients 
for  the  different  spans  confirms  the 
rationality  of  the  relations  assumed  above. 
Introducing  the  empirical  constants  in 
those  relations,  we  obtain  the  following 
formulae  for  suspension  bridges: 


.     (2) 


109 

ART.  16 
MAXIMUM  SPAN  FOR  CABLE 

The  theoretical  limiting  span  for  a 
suspension  bridge  is  the  span  at  which 
the  cable-section  becomes  infinitely 
large  in  proportion  to  the  load  it  can 
carry.  The  defining  equation  for  this 
condition  is,  therefore, 

— °=  oo  (1) 

9i 

where  g\  is  the  intensity  of  the  total 
load  suspended  from  the  cable. 

If  <70  =  the  weight  of  the  cable  per 
linear  horizontal  unit,  and  n  =  the  rise- 

/ 

ratio  =—,  the  maximum  tension  in  the 
L 

cable  will  be 

6w*.     (2) 
The  weight  g$  is  given  by  the  equation 


110 

where  s0  is  the  unit  working  stress  and 
7-0  is  the  weight  per  linear  foot  per  sq.in. 
of  cross-section  of  the  cable.  From  Eqs. 
(2)  and  (3)  we  obtain 


T 


(4) 

Introducing  the  condition  for  maximum 
span,  as  defined  by  Eq.  (1),  we  obtain 
the  relation 


Hence, 

Qo» 

==—  -     (5) 


This  equation  shows  that  the  maximum 
limiting  span  is  independent  of  the  live- 
load  or  weight  of  the  stiffening  truss. 
Equating  the  first  derivative  of  the 
second  member  of  (5)  to  zero,  we  find 


Ill 

the  rise-ratio   giving  the  absolute  max- 
imum span  to  be 


...     (6) 
With  this  value,  Eq.  (5)  becomes 

Zmax=  1.085^.       .       .        (50 

To 

Numerical  Values.  For  very  heavy 
cables,  the  weight  of  the  cable-wrapping 
may  be  neglected;  hence  ^0  is  simply 
the  density-factor  of  steel  =3.  4. 

The  extreme  limit  which  no  cable-span 
can  ever  exceed  is  that  for  which  s0 
equals  the  elastic  limit  of  the  best  cable 
material  or  s0=  180,000.  Eq.  (5')  then 
gives 

Extreme  Zmax=  65,520  ft.      .     (7) 

For  practical  purposes  it  is  necessary 
to  introduce  a  safety  factor  in  the 
working  stress;  reducing  the  latter  to 
§0  =  60,000,  we  obtain,  by  Eq.  (50, 

Zmax=21,S40  ft  .     .     .     (70 

This  span  with  a  rise-ratio  of  n  =  .306, 
would  require  towers  about  7000  ft., 


112 

high;    the  above  result,  therefore,  is  of 
no  practical  significance. 

Replacing  the  above  value  of  n  by  the 
economic  ratio 


and  retaining  s0  =  60,000,  Eq.  (5)  yields 
Practical  Jmax=15,160  ft  .     (1") 

This  value  gives  the  limit  of  span 
which  may  be  approached,  but  not 
exceeded,  by  successively  reducing  the 
amount  of  extraneous  load  for  any  given 
cable-section  or  by  increasing  the  cable- 

section  for  any  given  load  so  that  —  db  oo  . 

01 

At  the  maximum  span  given  by  Eqs. 
(7),  (7')  or  (7"),  the  cable-section  may 
have  any  finite  value  so  long  as  there 
is  no  load  suspended  from  it.  The 
addition  of  the  smallest  load  will  neces- 
sitate reducing  the  span  or  else  increas- 
ing the  section  A0  to  infinity. 

It  may  be  noted  that  the  limiting  span 
increases  directly  with  the  working 


113 

stress   SQ   and  inversely  with  the  cable- 
weight  factor  fo- 

In  comparison  with  the  above  limit- 
ing values,  it  is  of  interest  to  consider 
the  largest  existing  cable-span.  This 
is  a  cableway  at  Caperton,  W.  Va.,  built 
in  1898,  and  having  a  span  of  £  =  2100  ft., 
or  only  about  one-seventh  of  the  span- 
length  which  may  yet  be  attained. 

ART.  17 

MAXIMUM  SPAN   FOR  SUSPENSION 
BRIDGES 

From  Eq.  (2)  of  Art.  15,  we  obtain  the 
following  empirical  expression  for  the 
weight  of  the  cable  (C)  in  terms  of  the 
suspended  loading  and  the  length  of 
span  (I)  : 


Substituting  the  empirical  expressions 
for  8,  T  and  F  in  terms  of  the  live-load 
L,  Eq.  (1)  becomes,  practically, 

.068i(1.84L+  .35ZJ  +  1Q5Z2) 


. 


-.0075Z) 


114 

The  theoretical  maximum  span  for 
the  suspension  bridge  is  the  span  at 
which  the  cable-section  becomes  infinite. 
This  condition  is  realized  when  the 
denominator  of  Eq.  (2)  reduces  to  zero,  or 

Jmax  =  -  =  14,700  ft. 


This  is  the  upper  limit  of  feasible 
spans  for  suspension  bridges  and  repre- 
sents the  span  at  which  the  suspension 
bridge  ceases  to  be  self-supporting.  It 
is  somewhat  smaller  than  the  maximum 
span-limit  (15,160  ft.)  for  a  simple 
cable,  as  determined  in  the  preceding 
article,  simply  because  the  weight  of 
cable  wrapping  and  fastenings  was  not 
considered  in  that  investigation. 

Another  method  of  deducing  the 
limiting  span,  possessing  the  advantage 
of  greater  generality  inasmuch  as  it  is 
applicable  to  other  forms  of  bridge- 
structures,  is  as  follows:  Let  Ci=  the 
weight  of  the  cable  and  W\  =the  total 
suspended  load,  per  linear  foot,  for 
any  span  (li).  For  any  other  span 


115 

(Z),  the  weight  of  the  cable  is  given  by 
the  proportion 

C       (C+W)l 
' 


Solving  this  equation,  we  obtain 

C  WC*  (4) 

- 


For  C  =  GO  t  the  denominator  of  the  above 
expression  must  reduce  to  zero,  or 


This  formula  enables  the  limiting 
span  to  be  calculated  from  the  results 
of  any  single  design.1  In  the  designs  at 
hand, 

1=   1,500  2,250  3,000 

C=   1,286  2,160  3,720 

TF  =  11,162  12,522  14,418 

.'.  Zmax  =  14,300  15,300  14,600ft. 

1  The  same  formula,  with  C  denoting  the 
weight  of  the  arch-rib,  was  used  by  the  writer 
in  determining  the  maximum  spans  for  steel 
and  concrete  arches.  See  Thesis  submitted  for 
the  Degree  of  C.E.  at  Columbia  University. 


116 

The  practical  agreement  between  these 
values  indicates  the  reliability  of  the 
above  method  of  determining  the  max- 
imum span  from  a  single  design.  Taking 
the  mean  of  the  above  values,  there 
results 


a  value  identical  with  that  yielded  by  the 
first  method  of  this  article. 

Although  the  above  is  the  limiting 
feasible  span,  defined  by  C=  oo,  it  is 
evident  that  the  sections  will  become 
too  large  for  practical  construction  long 
before  that  length  of  span  is  reached. 
In  order  to  determine  the  practical 
maximum  span,  a  value  for  the  maximum 
cable-section  must  first  be  fixed. 

The  cables  of  the  three  largest  sus- 
pension spans,  viz.,  the  Brooklyn,  Wil- 
liamsburg  and  Manhattan  Bridges,  are 
15f,  18|  and  21^  inches  in  diameter, 
respectively.  Cables  with  a  diameter 
of  24  inches  were  used  in  one  of  the 
designs  in  this  investigation,  but  it  is 
doubtful  whether  any  larger  diameter 


117 

can  be  put  together  without  excessive 
difficulty  of  manipulation  and  uncer- 
tainty of  proper  distribution  of  stress 
among  the  different  strands. 

With  the  exception  of  some  old  chain 
bridges,  there  is  no  bridge  on  record 
with  more  than  six  cables.  Twice  that 
number,  or  four  groups  of  three,  were 
used  in  one  of  the  writer  's  designs,  but 
it  is  extremely  improbable  that  a  greater 
number  than  16  could  be  practically 
combined  in  one  structure. 

Assuming,  then,  a  section  of  16  cables 
of  24  inches  diameter  for  the  bridge  of 
maximum  span,  we  have 


max 


=  20,000  Ibs. 


Solving  Eq.  (2),  Art.  15,  for  the 
length  of  span  in  terms  of  the  cable- 
weight  and  live-load,  there  results 

^ 


Substituting  in  this  equation  the  max- 
imum value  of  C,  as  just  established,  and 
.assuming  different  values  of  the  live- 


118 

load,    we    obtain    the    following    values 

for  the  maximum  span : 

For 

L  =  0,  Zmax=  9,500  ft. 

L=  10,000,  Zmax=4,900  ft- 

L=  15,000,  Zmax=4,000ft. 

L  =  20,000,  Cax^3;500  ft- 

The  first  of  the  above  results  simply 
signifies  that  9500  ft.  is  the  span  at  which 
the  cable  will  just  be  able  to  support  the 
wind-bracing.  As  this  condition  is  one 
of  zero  loading,  it  may  be  omitted  from 
practical  consideration.  Furthermore, 
it  is  hardly  probable  that  a  structure 
of  the  magnitude  under  investigation 
would  ever  be  planned  for  a  lighter 
loading  than  about  10,000  Ibs.  per  linear 
foot,  particularly  when  it  is  remembered 
that  this  would  require  about  10  Ibs.  of 
steel  for  every  pound  of  useful  load. 

It  will  therefore  suffice  to  restrict 
the  conditions  of  the  problem  to  the 
practical  limits  of  L  =  10,000  to  L  =  20,000 
Ibs.  of  live-load  per  linear  foot.  We 
thus  find  that  the  maximum  practical 


119 

span  for  suspension  bridges  ranges  from 
3500  to  4900  ft.,  depending  upon  the 
assumed  live-load. 

ART.  18 

EMPIRIC  FORMULA  FOR  COST  OF 
SUSPENSION  BRIDGES 

The  expression  for  the  cost  of  any 
span  (/)  will  be  assumed  of  the  general 
form 

...     (1) 


Since  we  have  but  three  values  deter- 
mined for  C  by  actual  design,  the  for- 
mula is  limited  to  an  equal  number  of 
terms. 

From    the    results    of    the    preceding 
estimates,  we  have 

C  =  $ll,645,000  for  Z=  1500  ft. 
C  =  $23,760,000  for  I  =  2250  ft. 
C  =  $46,785,000  for  Z  =  3000  ft. 

Substituting  these  values  in  (1),  and 
solving  the  resulting  three  equations 


120 

for  the  unknown  coefficients,  we  obtain 
C  =  8900Z-3.77Z2  +  .0020Z3.     .     (2) 

as  the  general  cost-formula  for  suspen- 
sion bridges.  This  gives  the  combined 
cost  of  steel  work  and  substructure  for 
any  span  for  an  assumed  live-load  of 
18,000  Ibs.  per  linear  foot.  For  any 
other  loading,  the  above  coefficients 
should  be  changed  in  proportion. 

ART.  19 

ECONOMIC  SPAN  FOR  SUSPENSION 
BRIDGES 

As  established  in  the  preceding  article, 
the  cost  of  a  suspension  bridge  is  given 
by  the  expression 


C  =  8900Z-3.77Z2  +  .0020Z3.     .     (1) 

Of  this  cost,  about  65  per  cent  repre- 
sents the  steel  work  and  the  remainder 
provides  for  the  masonry  and  anchorages. 
A  study  of  the  contracts  for  recent 
long-span  bridges  shows  an  additional 
cost  of  about  20  per  cent  for  pavements, 


121 

tracks,  railings,  ornamental  work,  elec- 
tric lighting,  etc.  To  this  must  be  added 
the  cost  of  terminal  structures  and  real 
estate  for  the  approaches.  In  a  city 
structure  the  last  item,  as  in  the  case 
of  the  Manhattan  Bridge,  may  amount 
to  more  than  the  cost  of  the  bridge 
itself.  A  fair  average  value  for  this 
item  is  about  100  per  cent.  Adding  the 
above  items,  we  find 

Total  first  cost  of  bridge  =  220%  C.    (2) 

The  rate  of  interest  will  be  assumed  at 
5  per  cent.  The  cost  of  maintenance, 
including  repairs,  painting,  lighting,  etc., 
averages  about  4^  per  cent  of  the  cost 
of  the  superstructure.  In  addition,  a 
certain  annuity  must  be  set  aside  for 
the  periodic  renewal  of  the  superstructure. 
The  foundations  may  be  permanent, 
but  the  steel  work  has  a  limited  life. 
The  life-periods  of  various  suspension 
bridges,  or  the  periods  before  recon- 
struction or  removal,  whether  terminated 
by  failure  or  increased  traffic  demands, 
have  been  as  follows: 


122 

1827  1  Hammersmith  (London)  .55  years. 
1829  2  Regnitz  (Bamberg)  ...  .59      " 

f  1  O  it 

1834  2  Freiburg  (Switzerland)  fir       , , 

1839  *  Weser  (Hamlin) 51      li 

1845  l  Neckar  (Mannheim) 46      " 

1850  Fairmount  (W.  Va.)  .  .  .40      " 

1851  3  Niagara    (Old   S.   B.    at 

Lewiston) 13      " 

1852  4  Charleston  (W.  Va.) ....  52      " 
1855  3  Niagara  Falls    (Railway 

Bridge) 42      ' ' 

1867  5  Cincinnati  (Ohio  R.)  .  .  .31      " 

1868  *  Moldau  (Prague) 32      " 

(     1  Q  « 

1869  3  Niagara    Falls    (Hwy. 

Bridge) 

1877  6  Point  Bridge  (Pittsburg)  .28 

Mean  Life  Period 31  years. 

xMelan,  " Konstruktion  der  Hangebriicken >k 
(Leipzig,  1906),  p.  204. 

2  Nouv.  aim.  de  la  constr.,  1881.    Also  Riese, 
"Die  Ingenieurbauwerke  der  Schweiz." 

3  Eng.  Record,  1897  (Apr.  24);  1899  (Aug.  26). 

4  Eng.  News,    1905   (Feb.  2).     Eng.   Record, 
1904  (Dec.  24). 

5  Eng.  Record,  1898  (Sept.  10,  Nov.  26). 

6  Eng.  Record,  1905  (May  6-13). 


123 

This  value ,  or  30  years  in  round  numbers, 
will  be  adopted  as  the  probable  life  of 
the  steel  work  of  a  suspension  bridge. 
It  is  true  that  the  newer  bridges  possess 
the  advantages  of  improved  material 
and  construction,  but  the  more  severe 
traffic  to  which  they  are  subjected  and 
the  smaller  margin  of  safety  provided 
in  their  design  prevent  them  from  attain- 
ing as  long  a  life  as  some  of  the  old 
structures.  For  a  railroad  bridge  strained 
to  its  full  capacity,  the  above  value  of 
the  life-period  is  certainly  not  too  small. 
At  5  per  cent  compound  interest,  a 
sinking  fund  to  meet  the  cost  of  re- 
newal in  30  years  will  require  an  annuity 
of  1.505  per  cent.  (See  Annuity  Tables.) 
The  annual  charge  against  the  bridge 
will  therefore  consist  of  the  following 
items : 

Interest  charge  =    5%  X 220%  C  =  ll%C 

Repairs    and    mainte- 
nance      =4.5%  X   65%  C=  3%  C 

Depreciation  =  Annuity  for  renewal  in 

30  years  =  1.505%  X  65%  C  =   1%  C 

Total  annual  charge  =15%  C 


124 

The  limiting  economic  span  is  that 
at  which  the  revenue  from  traffic  (T) 
just  balances  the  annual  cost  of  the 
structure.  We  may  therefore  write 

15%C=T.      ...     (3) 

as  the  defining  condition  for  the  economic 
span. 

In  determining  the  maximum  traffic 
returns  (T)  to  be  expected  from  a  long- 
span  bridge,  we  are  guided  by  the 
following  considerations :  The  Brooklyn 
Bridge  now  carries  about  118,000,000 
paid  passengers  per  annum.1  The  max- 
imum daily  is  30  per  cent  greater  than 
this  rate  and  the  maximum  hourly 
is  500  per  cent  greater  still.2  The 
Williams  burg  Bridge,  opened  20  years 
later,  is  a  close  competitor,  with  a  pas- 
senger traffic  of  75,000,000  per  annum3; 
at  the  present  rate  of  increase,  it  will 

1  Report    of    Public    Service    Comm.,     1st 
District,  N.  Y.,  1909. 

2  Engineering  Record,  1910  (June  11). 

3  Engineering  News,  1910  (Jan.  27). 


125 

soon  equal  the  older  structure  in  volume 
of  traffic.  The  usefulness  of  both  these 
structures  is  steadily  growing,  despite 
the  opening  of  several  competing  routes 
of  communication  across  the  same  river. 
Each  bridge  helps  to  build  up  the  dis- 
tricts which  it  connects,  thereby  creat- 
ing increased  traffic  for  itself.  Thus 
there  were  9,000,000  passengers  crossing 
the  Brooklyn  Bridge  in  1884,1  42,000,000 
passengers  in  1893,1  and  118,000,000 
passengers  in  1909.2  The  total  number 
of  passengers  annually  crossing  the 
East  River  increased  500  per  cent  in 
the  17  years  after  the  opening  of  the 
Brooklyn  Bridge,3  and  240  per  cent 
more  since  the  Williamsburg  Bridge 
was  opened.4  These  facts  indicate  that 

1  Statement  of  Chas.  Macdonald  to  Bd.  of 
Eng.   Officers,   1894;    also  Engineering  Newsr 
1893  (Feb.  23). 

2  Report    of     Public    Service     Comm.,     1st 
Distaict,  N.  Y.,  1909. 

3  Lindenthal    in  Discussions  at   the   N.   Y.. 
R.  R.  Club,  Apr.  18,  1901. 

4  Engineering  News,  1910  (Jan.  27). 


126 

any  large  bridge,  if  judiciously  located, 
will  ultimately  get  all  the  traffic  it  can 
.accommodate. 

In  the  absence  of  any  better  guide, 
let  us  take  the  amount  of  travel  on  the 
Brooklyn  Bridge  as  the  maximum  traffic 
to  be  expected  on  any  other  long-span 
structure.  This  value  may  justly  be 
augmented  by  50  per  cent  for  the  greater 
capacity  of  a  six-track  bridge,  but  this 
additional  profit  will  be  disregarded  to 
compensate  for  the  early  years  of  un- 
developed traffic.  We  will  therefore 
assume  118,000,000  passengers  using 
the  bridge  in  a  year.  For  a  span  of  the 
length  under  consideration,  a  toll  of 
5  cents  per  passenger  would  be  an 
equitable  rate.  The  same  charge  is 
now  made  for  ferry  or  tunnel  transporta- 
tion across  the  Hudson  River,  and  bridge 
travel  would  surely  be  preferred  for  its 
greater  speed  and  comfort. 

At  night,  when  the  passenger  traffic  is 
a  minimum,  the  tracks  can  be  used  for 
the  transportation  of  freight.  There 
are  about  6000  cars  of  freight,  inbound 


127 

and  outbound,  at  Jersey  City  daily, 
and  about  half  of  this  belongs  to  New 
York.  We  may  therefore  safely  count 
on  at  least  1500  cars  of  freight  daily 
crossing  a  six-track  bridge  over  the 
Hudson  River  or  any  similar  location. 
The  total  annual  traffic  over  a  long- 
span  bridge  may  therefore  attain  the 
following  value: 

118,000,000  passengers  at  5  cents  =  $5,900,000 
547,500  cars   of  freight  at   $4=   2,190,000 


/.  T= total  annual  revenue  =$8,090,000 

Substituting  this  value  in  eq.  (3),  we 
obtain 

C=  $54,000 ,000 

as  the  maximum  economic  cost  for  a 
long-span  bridge.  With  this  value  of 
C,  the  solution  of  eq.  (1)  yields 

Economic  1  =  3170  ft. 

In  the  case  of  the  proposed  Hudson 
River  Bridge,  of  somewhat  shorter  span, 
calculations  indicated  a  profit  of  less 


128 

than    1    per   cent    on   the   investment,1 
thus  confirming  the  above  result. 

Conclusion.  The  limiting  economic  span 
for  suspension  bridges  is  about  3170  ft., 
and  will  be  less  wherever  the  probable 
traffic  returns  are  smaller  than  assumed 
in  this  investigation. 

1  H.  G.  Prout  in  Discussions  at  the  N.  Y. 
Railroad  Club,  Apr.  18,  1901. 


129 


CHAPTER  V 

STUDY   OF    CANTILEVERS 

ART.  20 

CANTILEVER  BRIDGES — HISTORICAL 
SKETCH 

IN  adaptability  to  long  spans  and 
possibility  of  erection  without  false- 
work, the  cantilever  is  the  sole  compet- 
itor of  the  suspension  bridge.  Both  of 
these  types  have  attained  prominence 
by  remarkable  examples  of  design  and 
construction.  With  but  one  exception, 
however,  the  suspension  type  has  never 
been  employed  for  fast  railway  traffic. 
Its  use  has  been  confined  to  highway 
bridges  or  wherever  aesthetic  require- 
ments prevailed.  The  banner  bridges 
of  the  suspension  type,  those  over  the 
East  River,  have  been  attributed  to 
"  an  ingrained  fad  of  the  New  York 


130 

Department  01  Bridges."  For  long  rail- 
way spans,  the  cantilever  has  almost 
invariably  been  given  the  preference  on 
account  of  its  superior  rigidity  at  a 
given  cost.  The  longest  span  in  the 
world  (Forth  Bridge  1710  ft.)  is  of  the 
cantilever  form,  and  the  Quebec  Bridge, 
now  under  construction,  will  raise  the 
record  for  length  of  span  to  1800  ft. 
•  Although  cantilever  design  is  a  com- 
paratively recent  development  in  en- 
gineering, the  idea  is  by  no  means  a  new 
one.  Bridges  of  logs,  put  together  on 
the  cantilever  principle,  have  been  used 
in  tropical  countries  since  prehistoric 
times.1  In  1783,  a  wooden  cantilever 
bridge  of  112-ft.  span  was  reported  by 
travelers  in  Thibet.2  An  1800-ft.  "  fly- 
ing pendant  lever  bridge  "  to  cross  the 
East  River  and  a  3000-ft.  span  across 
the  North  River  were  proposed  by 
Pope  in  1810.3  Fairbairn's  proposal 

1  Van  Nostrand's  Magazine,  Jan.,  1886. 

2  Pope,    Treatise    on    Bridge    Architecture, 
New  York,  1811. 

3  Ibid. 


131 

for  the  Britannia  Bridge,  in  1845,  was 
a  cantilever  design.1  Stephenson,  in 
1846,  and  Edwin  Clark,  in  1850,  sug- 
gested the  cantilever  idea.2  In  the 
latter  year  Sir  John  Fowler  built  a 
wooden  model  to  illustrate  the  form  of 
construction.3  In  1859  Prof.  Ritter  of 
Hanover  proposed  cutting  the  chord  of 
a  continuous  truss  at  the  points  of  con- 
traflexure  and  worked  out  the  stresses 
in  the  resulting  cantilever  structure 
for  a  span  of  526  ft.  The  first  canti- 
lever design  actually  constructed,  how- 
ever, was  a  bridge  of  124  ft.  span  over 
the  Main  River  near  Hassfurt,  designed 
and  built  by  Gerber  in  1867.4  On  this 
account,  cantilevers  are  known  as  "  Ger- 
ber Bridges "  on  the  continent.  In 
1871,  Fowler  and  Baker  built  two 
cantilever  spans  of  800  ft.  over  the 
Severn,  and  in  1873  Baker  designed  a 

1  Engineering  (London),  Mar.  5,  1886. 

2  Engineering  (London),  Feb.  28,  1890. 

3  Proc.  of  the  Inst.  of  C.  E.,  IX,  p.  256. 

4  Mehrtens,  "Der  deutsche  Briickenbau  im 
19.     Jahrundert,"  Berlin,  1900. 


132 

cantilever  ferry  bridge  of  650  ft.  span 
over  the  Tees.1  The  first  cantilever 
bridge  for  railway  traffic,  a  span  of  148 
ft.,  was  built  in  1876  over  the  Warthe 
at  Posen.2  In  the  same  year,  the  first 
American  cantilever,  the  Kentucky  Via- 
duct, was  built  by  C.  Shaler  Smith.3 
In  this  structure  and  in  the  Niagara 
Cantilever  built  in  1883  by  C.  C.  Schneider 
for  the  Michigan  Central  Railroad,  the 
possibility  of  erection  without  false- 
work was  first  demonstrated.4  In  1881, 
four  years  after  the  completion  of  the 
Kentucky  Viaduct,  the  final  designs 
for  the  Forth  Bridge  were  approved. 
The  successful  completion  of  that  re- 
markable structure  in  1889  5  marked  the 
end  of  the  experimental  period  for  the 
cantilever  and  served  to  fix  that  type 
in  its  present  dominant  position  in 
long-span  construction. 

1  Engineering  News,  Nov.  24,  1904. 

2  Engineering  (London),  Feb.  28,  1890. 

3  Trans.  Am.  Soc.  of  C.  E.,  Nov.,  1878. 

4  Trans.  Am.  Soc.  of  C.  E.,  Nov.  1885. 

5  Engineering  (London),  Dec.  6,  1889. 


133 

A  table  of  the  most  noted  cantilever 
bridges  with  their  principal  dimensions 
is  appended.  It  will  be  observed  that 
only  three  cantilevers  exceed  1000  ft. 
in  span,  whereas  eight  suspension  bridges 
have  exceeded  this  value.  It  is  mainly 
between  the  limits  of  500  and  1000  ft. 
that  cantilevers  predominate.  The  high 
values  of  the  ratio  of  dead-load  to  live- 
load  are  significant,  indicating  a  greater 
expenditure  of  metal  than  is  required  in 
suspension  bridges. 

It  will  also  be  noticed  that  there  are 
comparatively  few  cantilevers  below  500 
ft.  span,  that  being  the  domain  of  the 
ordinary  truss.  With  increasing  span- 
length,  however,  the  cantilever  bridge 
becomes  superior  to  the  simple  truss  be- 
cause of  the  increasing  significance  of 
the  following  advantages. 

1.  No    obstruction    of    the    channel 
during  erection  and  the  saving  of  the 
cost  of  falsework. 

2.  Lower    economic    depth    of    truss. 

3.  Smaller  required  width  resulting  in  a 
saving  in  the  piers  and  in  the  floor  system. 


134 

TABLE  II— NOTABLE 


Date. 

Name. 

Location. 

Engineer. 

1908 

1  Quebec 

St  Lawrence  R. 

Cooper 

1889 

Forth 

Scotland     .... 

Fowler  &  Baker 

1908 

Queensboro.  . 
Lansdowne 

EastR.,  N.  Y... 
India     

Dept.  of  Br. 

1903 

j[  Monongah  ela 

Pittsburg 

Boiler  &  Hodge 

1892 

Memphis  .... 

Mississippi  R.  .  . 

Morison  

1910 

Beaver  

Ohio  R.,  Pa  

1903 

Ohio  R  

Boiler  &  Hodge 

1905 

Thebes  

Miss.  R.,  111.  ... 

Modjeski         & 
Noble 

1904 

Ruhrort     .  .  . 

Rhine   R  ,    Ger- 

1891 

Red  Rock 

Colorado  R 

1902 

Marietta 

Ohio  R    Ohio 

1902 

1887 

Czernavod  .  .  . 
^  Poughkeepsie 

DanubeR  
Hudson  R 

1906 

Long  Lake 

New  York  

1903 
1897 

Connel  Ferry. 
Francis 
Joseph  .... 

Scotland  
Budapest  

Barry  

1883 
1876 
1883 

Niagara  
3  Kentucky  R. 
Fort  Snelling 

Niagara  Falls.  .  . 
Ohio  
Mississippi     R., 
Minn  

Schneider  
C.  S.  Smith  

Schneider  

1  Collapsed  1908,  before  completion. 

2  Reconstructed  1906. 


4.  More  favorable  distribution  of  the 
dead-load,  the  material  being  massed 
toward  the  piers. 


135 


CANTILEVER  BRIDGES 


Loading. 

Sp'n 
=  L 

S.S. 
=1 

C.A. 

=  771 

A.A. 

=  n 

Width 

Depth. 

L.L. 

D.L. 

D.L. 

L.lT 

1800 

675 

562  £ 

500 

67 

98-315 

13000 

26000 

2.0 

1710 

350 

680 

680 

32-120 

50-350 

4480 

21000 

4.7 

1182 

0 

591 

630 

60 

45-185 

8440 

27000 

3.2 

820 

200 

310 

248 

812 

360 

226 

346 

32 

60-126 

9000 

9000 

1.0 

790 

452 

169 

621 

30 

78 

4000 

7000 

1.75 

769 

285 

242 

320 

11000 

700 

310 

195 

298 

9000 

8000 

0.9 

671 

366 

152i 

521 

32 

50-75 

8000 

10000 

1.25 

667 

443 

112 

390 

36 

46-82 

660 

25 

650 

270 

300 

600 

27 

623 

548 

208 

170 

525' 

30 

38-75 

6000 

525 

175 

175 

0~ 

24 

20-60 

920 

840 

0.9 

524 

232 

146 

106 

21 

30-118 

4000 

7620 

1.9 

514 

102 

,206 

257 

6000 

495 

120 

187i 

20  7i 

28 

3000 

375 

300 

75 

375 

18 

38 

2530 

0.85 

315 

105 

105 

105 

3  Replaced  by  truss  bridge,  1910. 


5.  More  favorable  distribution  of  the 
wind-load,  for  the  same  reason. 

6.  Decreased   wind-load   stresses. 


136 

In  order  to  establish  data  for  deter- 
mining the  economic  and  maximum 
spans,  complete  designs  and  estimates 
will  be  made  for  cantilevers  of  three 
different  spans:  1000,  1500  and  2000 
ft.,  respectively.  The  condition  of  load- 
ing and  specifications  for  allowable 
working  stresses  will  be  assumed  the 
same  as  for  the  suspension  bridges  pre- 
viously designed. 

Before  we  can  proceed  with  the  design 
of  the  cantilevers,  it  is  necessary  to 
find  the  most  favorable  solutions  of  the 
following  problems. 

1.  Economic    span-ratios    for     canti- 
levers. 

2.  Economic    width    for    cantilevers. 


ART.  21 

ECONOMIC  SPAN-RATIOS  FOR 
CANTILEVERS 

Let    Z  =  length   of  suspended  span; 
m  =  length  of  cantilever  arm; 
n  =  length  of  anchor  arm. 


137 

Then    the    total  channel    span  will    be 

L-Z+2m   ....     (1) 

and  the  total  length  of  structure  will  be 

...      (2) 


Assuming  that  the  weight  per  linear  foot 
of  truss  in  any  span  or  arm  is  equal  to 
some  constant  factor  times  the  length  of 
that  span  or  arm,  let 

a  =  suspended  span  factor; 
6  =  cantilever  arm  factor; 
c  =  anchor  arm  factor. 

Then  the  weight  of  the  whole  structure 
will  be 

W=aP  +  2bm2+2cn2   .     .     (3) 
This  will  be  a  minimum  for 

al  =  bm  =  cn      ...     (4) 

Hence  the  economic  lengths  of  the  sus- 
pended span,  cantilever  arm  and  anchor 
arm  are  inversely  proportional  to  the 


138 

respective  dead  -load  factors;  in  other 
words,  the  economic  lengths  are  such  as 
to  make  the  weight  per  linear  foot  uniform 
over  all  parts  of  the  bridge. 

From  (1),  (2)  and  (4)  we  obtain  l 

1-     b        T 

I/  —  7       ^     *  JLJ  .         ffli— 


7       ^         LJ  .  li—  ^  -  ™  —  • 

b+2a  b+2a 


Numerical  Values.  The  weight  fac- 
tors a,  6  and  c  should  be  obtained  by 
actual  computation  of  weights  of  struc- 
tures similar  to  those  under  considera- 
tion. The  resulting  values  will,  of  course, 
be  found  to  vary  more  or  less  with  dif- 
ferent loadings  and  span-ratios.  By 
omitting  from  consideration  all  spans 
of  unusual  proportions,  and  reducing 
the  results  to  a  common  assumed  load- 
ing (=18,000  Ibs.  per  linear  foot  as  in 
the  following  designs),  the  writer  obtained 

1  Cf.  Burr's  solution  of  the  problem  in  his 
"  Stresses  in  Bridges  and  Roof  Trusses,  etc." 
(Wiley,  1908),  App.  V.,  p.  472. 


139 

the  following  average  values  of  the  truss- 
weight  factors: 

a  =14,  6  =  42,  c  =  21.! 

Substituting  these  values  in  Eqs.  (5),  we 
obtain 

Z=0.60  L,  ra  =  0.20  L,  n  =  0.40  L, 

for  the  economic  span-ratios  of  a  canti- 
lever bridge.  Prof.  Burr2  recommends 
values  of 

Z=0.5  to  0.55  L;     ra=0.20  L; 
n  =  0.42  to  0.5  L. 

An  exact  theoretical  solution  of  the 
problem,3  eliminating  the  use  of  em- 
pirical constants,  shows  that  the  total 
moment  areas  will  be  a  minimum  for 

Z=0.68L;     w=0.16L,     n  =  0.37  L. 

1  Compare  these  values  with  those  yielded 
by  the  writer's  designs,  viz.:   a=13.6,  6  =  42.3, 
c=21.7. 

2  Burr's  "  Stresses    in     Bridges    and     Roof 
Trusses,    etc."      (Wiley,     1908),     App.    V,    p. 
472. 

3  Marburg  in   Proc.  of  Eng.   Club   of  Phila., 
July,  1896. 


140 

This  solution  is  practically  defective, 
however,  in  disregarding  the  web-mem- 
bers and  lateral  bracing  and  in  assuming 
uniform  dead-load  over  the  whole  struc- 
ture. 

A  study  of  the  spans  of  the  cantilevers 
tabulated  in  a  preceding  article,  omitting 
.  those     of    extraordinary    form,     yields 
the  following  results : 
Extreme  values: 

l/L  m/L  n/L 

.20 -.66     .17 -.40     .28 -.78 

Mean  values: 

.38  .31  .45 

These  values  compared  with  those 
established  above  indicate  that, 
in  past  practice,  the  suspended  span 
as  a  rule  has  been  made  too  long  and 
the  cantilever  arms  too  short  for  the 
best  economy. 

For  the  designs  in  this  investigation, 
the  writer  has  adopted  a  compromise 
between  the  dictates  of  theory  and  those 
of  conformity  with  past  practice.  The 


141 

lengths  of  the  suspended  spans  will  be 
made  for 

L=1000         1500         2000, 
1=  500  650  800, 


so  that 

l/L=    0.5          0.43         0.4. 

The  suspended  span  is  thus  made  a 
diminishing  fractional  part  of  the  total 
span  as  the  latter  increases  in  length; 
otherwise  the  length  of  the  suspended 
truss  would  become  prohibitive  before 
the  limiting  cantilever  span  is  reached. 
(See  Art.  26.) 

The  lengths  of  the  anchor  arms  will 
be  made 


thereby  conforming  with  the  ratio  indi- 
cated by  both  theory  and  practice. 
This  determination  of  the  best  length 
for  the  anchor  arm,  however,  is  purely 
academic  as,  in  any  actual  design  of  a 
cantilever,  the  location  of  the  piers  is 


142 

determined  by  natural  conditions  and 
the  requirements  of  navigation  rather 
than  from  any  theoretical  investigations. 

ART.  22 
MINIMUM  WIDTH  FOR  CANTILEVERS  1 

On  account  of  the  saving  in  piers  and 
floor  members,  it  is  desirable  that  the 
width  of  any  bridge  structure  should  be 
a  minimum  consistent  with  the  demands 
of  lateral  rigidity.  In  simple  truss 
bridges  it  is  generally  considered  that 
adequate  stiffness  is  provided  by  a 
distance  c.  to  c.  of  trusses  of  ^  of  the 
.span.  The  minimum  width  for  canti- 
levers may  then  be  defined  as  that  width 
which  will  insure  the  same  degree  of 
rigidity  as  the  above. 

Using  the  same  notation  as  in  the 
preceding  article,  the  total  length  of 
span  for  a  cantilever  bridge  is  denoted  by 

L  =  l  +  2m      .     .     .     .(1) 

1  Adapted  from  an  analysis  given  to  his 
classes  by  Prof.  Burr. 


143 


If  a  lateral  load,  p  per  linear  foot,  acts 
on  the  structures,  the  central  deflection 
will  be 


~El384,        2  3        8 
This  reduces  to 


and 


for  Z  =  0.5L 
for  l  =  OAL 


.     (3) 


In  a  simple  truss  of  span  V  the  central 
deflection  is  given  by 

h-—-~r*  (& 

~384  El 

With  equal  rigidity,  the  simple  truss 
and  the  cantilever  must  suffer  the  same 
deflections.  Equating  the  right-hand 
members  of  Eqs.  (3)  and  (4),  there  .result 

Z'  =  .668L     for     Z  =  0.5L  ] 
and  [    .     (5) 

r  =  .701L     for     1  =  0  AL 


144 

The  distance  c.  to  c.  of  trusses  should 
not  be  less  than 

r 
"=18' 

or,  substituting  the  relations  of  Eq.  (5) 

Minimum  w==—  to  —L.     .     (6) 
£i         Zo 

It  is  interesting  to  note  here  that  the 
mean  width-ratios  for  the  structures 
listed  in  the  Table  of  Cantilevers  is 


a  value  on  the  safe  side  of  the  required 
ratio. 

In  the  designs  at  hand  a  ratio  of  w  = 

—  L  will  be  adopted  except  in  the 
«o 

shortest  span  where  the  required  space 
for  the  roadway  will  necessitate  a 
slightly  greater  width-ratio,  namely, 


145 


BIBLIOGRAPHY   ON   CANTILEVERS 

Quebec. 

Engineering  (London),  1900  (II,   189,  241); 

1902   (II,  419);    1903   (I,   92);     1905   (II, 

Sept.  22). 

Canadian  Engineer,  1902  (May). 
Engineering   News,    1897    (Oct.    14);     1902 

(Nov.  20);    1905  (Sept.  14);    1906  (July 

6);    1907  (Oct.  31). 
Engineering  Record,  1905  (Mar.  4,  Apr.  1, 

Apr.  8,  Sept.  16);  1906  (June  23,  Dec.  29); 

1908  (Mar.  14,  Apr.  25);    1910  (Sept.  24, 

Oct.  1,  Oct.  15). 
Railroad  Gazette,  Vol.  XXXIX,  No.  11. 

Forth. 

Engineering  (London),  1882  (Sept.  1,  8); 
1883,  1884,  1885  (Feb.  6);  1886,  1887, 
1888,  1889  (Dec.  6);  1890  (Feb.  28,  pp. 
213-283). 

Queensboro. 

Engineering  Record,  1901  (Mar.  16);  1902 
(Dec.  13);  1903  (Feb.  28,  Aug.  22);  1904 
(Mar.  3);  1905  (Mar.  4,  18,  May  20,  27, 
June  10);  1906  (Jan.  6,  27,  Feb.  10,  17, 
24,  Mar.  3,  17,  Sept.  15);  1907  (Dec.  21); 
1908  (Apr.  11,  May  28,  Aug.  8,  Nov.  14). 

Engineering  News,  1907  (Nov.  23);  1908 
(Nov.  12,  19). 

Iron  Age,  1907  (Mar.  7). 


146 

Railroad    Gazette,    1901    (Aug.    16);     1903 

(Oct.  2). 
Scientific  American,  1903  (Sept.  19). 

Marietta  (Ohio). 

Engineering  News,  1902  (Nov.  20). 
Engineering  (London),  1902  (II,  p.  418), 
Engineering  Record,  1903  (Sept.  26). 
Railroad  Gazette,  1902  (July  11). 

Monongahela  (Pittsburg). 

Engineering  News,  1902  (Nov.  20). 
Engineering  (London),  1902  (II,  p.  417). 
Railroad    Gazette,    1902    (Mar.    14);     1903 

(Aug.  14). 

Engineering  Record,    1902,    1903    (Jan.   3); 
1904  (Mar.  5,  Apr.  2,  Apr.  9). 

Memphis  (Tenn.). 

Engineering  News,  1892  (Feb.  27,  Mar.  12, 
May  12,  June  16,  Aug.  11,  Sept.  15). 

Mingo  Junction. 

Engineering  News,  1902  (Nov.  20). 
Engineering  (London),  1902  (II,  p.  417). 
Engineering  Record,  1904  (June  25,  July  2); 
1903  (Oct.  3). 

Thebes  (111.). 

Railway  Age,  1902  (June  20). 

Engineering  News,    1902    (Nov.   20);     1905 

(May  11). 
Engineering   (London),    1902    (II,    p.   416); 

1903  (I,  p.  326). 


147 

Engineering  Record,    1904    (Nov.   12,   Dec. 

24);      1905    (Mar.    4);      1905    (July    22, 

Sept.  16). 
Trans.  Assn.  of  Civ.  Eng.  of  Cornell  Univ., 

1905. 

Engineer  (London),  1905  (July  21). 
Railroad     Gazette,     1903     (Jan.    9);     Vol. 

XXXVIII,  No.  21. 

Ruhrort  (Germany). 

Schweizerische  Bauzeitung,  1904  (June  18). 
Engineering  (London),  1904  (II,  7,  35). 
Engineering  News,  1904  (July  14). 
Engineer  (London),  1907  (Nov.  1). 
Zeitschrift  d.  Ver.  Deutscher  Ing.,  1904  (July 
2). 

Connel  Ferry  (Scotland). 

Engineer  (London),  1903  (Sept.  11). 
Engineering  (London),  1903  (July  31). 
Engineering  Record,  1904  (July  2). 

Poughkeepsie  (N.  Y.). 

Engineering  (London),  1887  (May  13). 
Engineering  Record,    1905   (Oct.   28);     1906 
(Aug.  18). 

Long  Lake  (N.  Y.). 

Engineering  Record,  1906  (Sept.  29). 

Francis  Joseph  (Budapest). 

Zeitscrhrift  d.   Oesterr.   Ing.  u.  Arch.   Ver., 

1897  (Feb.  26). 
G<§nie  Civil,  1897  (May  8). 


148 

Engineer  (London),  1897  (May  14). 

Stahl  und  Eisen,  1898  (Feb.  1). 

La  Revue  Technique,  1898  (Sept.  25). 

Niagara. 

Trans.  Am.  Soc.  C.  E.,  Nov.,  1885. 
Engineering  (London),  1886  (Mar.  5). 
Engineering  Record,  1900  (Oct.  13). 
Scientific  American,  1900  (Oct.  20). 

Kentucky  R. 

Trans.  Am.  Soc.  C.  E.  Nov.,  1878. 
Engineering   Record,    1898    (July   9);     1910 
(Nov.  26). 


149 


CHAPTER  VI 
DESIGN   OF  CANTILEVERS 

ART.  23 

PRINCIPAL  DATA  FOR  DESIGN  OF 
CANTILEVER  BRIDGES 

No.  1.         No.  2.       No.  3. 

L=totalspan  =  ra  +  Z  ft-  ft.  ft. 

+  m                           =  1000  1500  2000 

1  =  suspended  span  =  500  650  800 

ra  =  cantilever  arm    =  250  425  600 

rc  =  anchor  arm          =  400  600  800 

w  =  width  c.  to  c.  of 

trusses  50  60  80 

d= depth     of     sus- 
pended truss           =  50-85  75-110  100-135 

h  =  depth  at  towers  =  150  225  300 

Load:  L.L  =  18,000  Ibs.  p.l.f. 
Wind=301bs.  per  sq.ft. 


Working  Stresses. 
Structural  steel 

MinL-ol   c+<wil 

Tension. 
20,000 

sn  nnn 

Compression' 
20,000 

1+P 

^SOOOr2 
30,000 

8000r2 


150 

For  erection  stresses,  the  above  may 
be  increased  by  20  per  cent. 

ART.  24 
ESTIMATE  OF  COST 

As  there  are  no  points  of  special  in- 
terest involved  in  the  design  of  the 
cantilever  bridges,  the  details  of  the 
computations  and  the  tables  of  stresses 
are  here  omitted.  The  total  quantities 
of  material  in  the  different  parts  of  the 
structures  are  presented  in  the  following 
estimates  of  cost.  In  these  estimates, 
the  same  unit  prices  are  used  as  in  the 
case  of  the  suspension  bridges.  (See 
Art.  14.) 


151 


CANTILEVER   BRIDGE   No.  1. 

(L=1000.) 
ESTIMATE  OF  COST. 


Material. 

Quantity. 
Ibs. 

Price. 

cts. 

Amount. 
$ 

Suspended  Span. 
Truss,  structural  steel  . 
nickel  steel  
Floor,  structural  steel  . 
Bracing,  struct,  steel  .  . 

1,446,400 
3,074,800 
2,837,500 
1,132,800 
246,000 

5.6 
8.0 
5.6 
5.6 
10.0 

80,998 
245,984 
158,900 
63,437 
24  600 

Total            

573  919 

Cantilever  Arm. 
Truss,  structural  steel  . 
nickel  steel  .... 
Floor,  structural  steel  . 
Bracing,  struct,  steel.  . 
^ins  nickel  steel  

2,051,000 
2,390,600 
1,426,000 
593,800 
179,200 

5.6 
8.0 
5.6 
5.6 
10.0 

114,856 
191,248 
79,856 
33,253 
17  920 

Total            

874  266 

Anchor  Arm. 
Truss,  structural  steel  . 
nickel  steel  .... 
Floor,  structural  steel  . 
Bracing,-  struct,  steel.  . 
Pins  nickel  steel  

2,559,400 
3,647  600 
2,280,000 
926,000 
223,500 

5.6 
8.0 
5.6 
5.6 
10  0 

143,326 
291,808 
127,680 
51,856 
22  350 

Total            

1  274  040 

'lower. 
Structural  steel  

5,472,000 

5.6 

306,432 

Steel  castings      ...... 

514  500* 

9  0 

46  296 

Total  

705,456 

152 


CANTILEVER  BRIDGE  No.  1. 

(L  =  1000.) 
ESTIMATE  OF  COST — (Continued). 


Material. 

Quantity. 
Ibs. 

Price. 

cts. 

Amount. 

$ 

Anchorage. 
Eye-bars  and  riveted 
work     

785,000 

5.0 

39  250 

Total            

78500 

Total  steel  work  

$3  506,181 

Main  Piers. 
Pier  masonry  (cu.yds.) 
Concrete  filling  in  crib- 
work       

7,590 
15,700 

$18 
7J 

136,620 
117,750 

Concrete  filling  in  cais- 

2,850 

12 

34200 

Timber    in    cribwork 
(B  M  )              

404  M 

45 

18,180 

Steel  in   caisson   and 

1,270,500 

4.5 

57,172 

Earth  excavation, 
(cu  yds  )  .        .... 

18,540 

$4 

74,160 

Total            

876,164 

Anchorages. 
Masonry  (cu.yds.).  .... 
Concrete  in  foundation 

Total              

.  12,370 
3,285 

$18 
12 

222,660 
39,420 

524,160 

Total  substructure 

$1  400  324 

Total  cost  of  bridge    .  . 

$4,906,505 

153 


CANTILEVER   BRIDGE   NO.   2. 

(L=1500.) 
ESTIMATE  OF  COST. 


Material. 

Quantity. 
Ibs. 

Price. 

cts. 

Amount. 

$ 

Suspended  Span. 
Truss,  structural  steel 
nickel  steel.  .  .  . 
Floor,  structural  steel  . 
Bracing,  struct,  steel. 
Pins  nicl'el  steel 

2,675,200 
5,731,800 
4,387,500 
2,264,000 
492  000 

5.6 
8.0 
5.6 
5.6 
10  0 

149,811 
458,544 
245,700 
126,784 
49  200 

Total        

1,030  039 

Cantilever  Arm. 
Truss  structural  steel, 
nickel  steel  .'  .  .  . 
Floor,  structural  steel  . 
Bracing,  struct,  steel.  . 
Pins,  nickel  steel  

5,365,400 
6,765,000 
2,960,000 
1,428,600 
432,300 

5.6 
8.0 
5.6 
5.6 
10.0 

300,462 
541,200 
165,760 
80,002 
43,230 

Total          

2  261  308 

Anchor  Arm. 
Truss,  structural  steel  . 
nickel  steel  .... 
Floor,  structural  steel  . 
Bracing,  struct,  steel  .  . 
Pins,  nickel  steel  

5,455,400 
8,631,600 
4,180,000 
1,852,200 
447,000 

5.6 
8.0 
5.6 
5.6 
10.0 

305,502 
690,528 
234,080 
103,723 
44,700 

Total  

2  757  066 

Tower. 
Structural  steel         .  . 

16  155  000 

5  6 

904  680 

1,324000 

9  0 

119  160 

Total  

2  047  680 

154 


CANTILEVER   BRIDGE   NO.  2. 

(L=1500.) 
ESTIMATE  OF  COST — (Continued}. 


Material. 

Quantity. 
Ibs. 

Price, 
cts. 

Amount. 
* 

Anchorage. 
Eye-bars    and   riveted 
Work     .    .    . 

1  794  100 

5  0 

89  705 

Total  

179  410 

Total  steel  work  

$8  275  503 

Main  Piers. 
Pier  masonry  (cu.  yds.) 
Concrete  filling  in  crib- 
work       

10,810 
24  560 

$18 
7i 

194,580 
184  200 

Concrete  filling  in  cais- 
son      

3  780 

12 

45  360 

Timber     in    cribwork 
(B.M.)  

558M 

45 

45  110 

Steel   in   caisson    and 
shafts         

1  682  000 

4  5 

75  690 

Earth  excavation 
(cu.  yds.)  

26,480 

4 

105,920 

Total  

1,261,720 

Anchorages. 
Masonry  (cu.  yds.)  
Concrete  in  foundations 

24,380 
6,450 

18 
12 

438,840 
77,400 

Total  

1,032,480 

Total  substructure 

$2  294  200 

Total  cost  of  bridge  .  .  . 

$10,569,703 

155 


CANTILEVER    BRIDGE   NO.    3. 

(L  =  2000.) 
ESTIMATE  OF  COST. 


Material. 

Quantity. 
Ibs. 

Price. 

cts. 

Amount. 

$ 

Suspended  Span. 
Truss,  structural  steel, 
nickel  steel  .... 
Floor,  structural  steel. 
Bracing,  struct,  steel.  . 
Pins,  nickel  steel  .  „  .  .  , 

5,142,800 
11,070,800 
7,456,000 
4,350,000 
944,800 

5.6 
8.0 
5.6 
5.6 
10.0 

287,987 
885,664 
417,536 
243,600 
94,480 

Total          

1  929  267 

Cantilever  Arm. 
Truss,  structural  steel  . 
nickel  steel  .... 
Floor,  structural  steel. 
Bracing,  struct,  steel.  . 
Pins,  nickel  steel  

13,116,200 
15,931,499 
6,204,000 
3,456,400 
1,042,000 

5.6 
8.9 
5.6 
5.6 
10.0 

734,507 
1,274,512 
347,424 
193,558 
104,200 

Total    

5  308  402 

Anchor  Arm. 
Truss,  structural  steel  . 
nickel  steel  .... 
Floor,  structural  steel  . 
Bracing,  struct,  steel.  . 
Pins,  nickel  steel  

11,136,200 
18,845,000 
8,272,000 
3,704,400 
894,000 

5.6 
8.0 
5.6 
5.6 
10.0 

623,627 
1,507,600 
463,232 
207,446 
89,400 

Total  

5,782  610 

Tower. 
Structural  steel 

37  638  000 

5  6 

2  107  728 

Steel  castings  

2,520,000 

9.0 

226  800 

Total  

4  669  056 

156 


CANTILEVER    BRIDGE   NO.   3. 

(L  =  2000.) 
ESTIMATE  OF  COST — (Continued}. 


Material. 

Quantity. 
Ibs. 

Price. 

cts. 

Amount. 

$ 

Anchorage. 
Eye-bars   and    riveted 
work 

3  374  300 

5.0 

168  715 

Total  

337,430 

Total  steel  work. 

Main  Piers. 
Pier  masonry  (cu.  yds.) 
Concrete  filling  in  crib- 
work  

17,860 
45,530 

18 
71 

$18,026,765 

321,480 
341,475 

Concrete  filling  in  cais- 
son 

6070 

12 

72  840 

Timber     in     cribwork 
(B.M  )        

820  M 

45 

36,900 

Steel    in    caisson    and 
shafts 

2  701  000 

4  5 

121  545 

Earth  excavation 
(cu.  yds.)  

45570 

$4 

182,280 

Total  

2,153,040 

Anchorages. 
Masonry  (cu.  yds.)  .  .  . 
Concrete  in  foundation 

45,950 
12,075 

$18 
12 

827,100 
144,900 

Total        

1  944,000 

Total  substructure. 

$4  097,040 

Total  cost  of  bridge    . 

$22,123,805 

157 


CHAPTER  VII 
CONCLUSIONS  FOR  CANTILEVERS 

ART.  25 

EMPIRIC    FORMULAE    FOR    WEIGHTS    OF 
CANTILEVER  SPANS 

LET  TI,  T2,  T3  =  truss-weights  per 
linear  foot,  in  suspended  span,  canti- 
lever arm  and  anchor  arm,  respectively; 
F  =  weight  of  floor,  per  linear  foot; 
LL  =  live  load  per  linear  foot. 

We  may  then  construct  semi-empiric 
formulae  for  the  truss-weights  from  the 
results  of  the  preceding  designs  as  follows : 

Suspended  Span.  The  weight  per 
linear  foot  of  a  simple  truss,  if  the  rel- 
ative dimensions  are  kept  fairly  con- 
stant, is  proportional  to  the  span  and  to 
the  total  load  carried.  Introducing  a 
factor  of  proportionality,  a,  we  have 

.      .     .     (1) 


158 

Applying  this  equation  to  the  preceding 
designs,  we  find 

a  =.00056,     .00053,     .00053; 
or,  as  a  mean  value, 

a  =  .00054. 

Cantilever  Arm.  The  weight  of  the 
cantilever  arm  may  be  considered  as 
composed  of  two  parts:  one  due  to  the 
reaction  of  the  suspended  span  applied 
as  an  end-concentration,  and  the  other 
due  to  the  weight  and  loading  of  the 
arm  itself.  This  relation  may  be  ex- 
pressed symbolically  as 


.     .     (2) 

The  results  of  the  preceding  designs, 
substituted  in   the   formula,   yield 

61  =  .00087     .00085     .00087 

62  =  •  00023     .00023     .00023 

or  as  mean  values, 

61  =  .00086 


159 

and 

62  =  .00023 

A  simpler  formula,  involving  but  one 
undetermined  coefficient,  may  be  con- 
structed from  the  observed  fact  that  the 
weight  per  linear  foot  of  the  cantilever 
arm  varies  with  the  total  loading  and 
with  the  square  root  of  the  channel 
span,  or 

T2  =  b(T2  +  F+LL).VL.  .     .     (3) 

The  constant  of  proportionality,  6,  is 
determined  from  the  preceding  designs  as 

6  =  .0133,     .0134,     .0134. 

The  close  agreement  between  these 
values  of  b  indicates  the  reliability  of 
the  above  formula  even  under  varying 
values  of  the  suspended  span  ratio. 
Taking  the  mean  value,  we  have 

6  =  .0134. 

Anchor  Arm.  A  rational  formula  for 
the  anchor  arm  would  involve  too  many 
factors  for  practical  usefulness.  A  simple 


160 

empirical  formula,  however,  is  suggested 
by  the  observation  that  the  weight  per 
linear  foot  of  the  anchor  arm  varies 
with  its  total  load  and  with  the  square 
root  of  its  length.  We  may  therefore 
write 

.     .(4) 


Substituting  the  results  of  the  pre- 
ceding designs,  eq.  (4)  yields 

c=.0190,     .0189,     .0191, 
or,  as  a  mean  value, 

c  =  .0190. 

As  the  total  amount  of  steel  is  not 
materially  affected  by  limited  changes 
in  the  form  or  proportions  of  the  trusses, 
and  as  variations  in  the  spans  and  in 
the  loading  are  fully  provided  for  in  the 
above  formulae,  they  may  properly  be 
applied  to  any  other  cantilever  bridges 
designed  for  any  live-load,  provided 
the  same  working  stresses  are  used. 
Whenever  improved  material  or  con- 
struction justifies  higher  unit  stresses, 


161 

the  empirical  constants  in  the  above 
formulae  should  be  reduced  in  the  in- 
verse proportion. 

ART.  26 

THEORETICAL  LIMITING  SPANS  FOR 
CANTILEVERS 

Maximum  Channel  Span.  A  solu- 
tion of  the  empiric  formula  for  the 
weight  of  the  cantilever  arm,  as  estab- 
lished in  the  preceding  article,  yields- 


This  expression  will  become  infinite 
when  the  denominator  reduces  to  zero, 
i.e.  when 


b     .0134' 
or 

L  =  5600. 

Hence  the  maximum  possible  span  for  a 
cantilever  bridge  is  5600  ft.  This  value 
may  be  approached,  but  never  exceeded 


162 

by  increasing  the  ratio  of  dead-load  to 
live-load  indefinitely. 

Note  that  the  corresponding  maximum 
span  for  the  suspension  bridge  is  14,700 
ft.,  or  about  2.6  times  as  great  as  the 
above. 

Maximum  Suspended  Span.  A  solu- 
tion of  the  empiric  formula  for  the  weight 
of  the  suspended  span,  as  established 
in  the  preceding  article,  yields 


r,  --.  i     .  .  (2) 

This  expression  will  become  infinite 
when  the  denominator  reduces  to  zero, 
i.e.,  when 


a     .00054 ' 
or 


Hence  the  maximum  possible  length  for 
the  suspended  span  is  1850  ft.  This 
^value  has  a  theoretical  significance  sim- 
ilar to  that  of  L  in  the  preceding  para- 
.graph. 


163 

Maximum  Length  of  Anchor  Arm.  A 
solution  of  the  empiric  formula  of  the 
preceding  article  for  the  weight  of  the 
anchor  arm  yields 


.     .     .     (3) 
1  —  cVn 

This    expression    becomes    infinite    for 

=  1=  JL 
c      .0190* 

Hence 

=2760. 


max 


The  limiting  length  of  anchor  arm  is 
therefore  2760  ft. 

Combining  the  above  values  of  limit- 
ing spans,  we  find  that  the  cantilever 
bridge  of  maximum  length  will  have  the 
following  proportions : 

Z=1850,     ra=1875,     n  =  2760 
L=Z+2ra  =  5600,  S=Z+2m+2n=ll,120. 

It  will  be  observed  that  Zmax  =  0.35Lmax. 
This  is  less  than  the  economic  ratio  for 
ordinary  spans  and  is  a  justification  of 
the  writer's  plan  of  reducing  the  relative 


164 

length  of  the  suspended  truss  as  the 
total  length  of  span  (L)  is  increased. 
It  is  also  seen  that  wmax=0.49Lmax,  a 
value  approximating  the  economic  ratio. 

ART.  27 

THEORETICAL  LIMITING  SPAN  FOR 
A  SIMPLE  TRUSS 

From  the  weights  obtained  for  the 
three  suspended  spans  in  the  foregoing 
designs  (Z  =  500,  650,  800  ft.),  the  limit- 
ing spans  for  ordinary  truss  bridges  may 
be  deduced.  A  correction  must  first 
be  applied,  however,  for  the  increased 
stresses  produced  in  some  of  the  members 
by  the  cantilever  method  of  erection. 
A  study  of  the  above  designs  indicates 
an  extra  truss-weight,  attributable  to 
these  erection  stresses,  of 

6.3%,     6.1%,     6.0%, 

respectively,  or,  as  an  average,  6.1  per 
cent  of  the  total  weight.  Consequently, 
for  a  given  span,  a  simple  truss  would 
weigh  about  6.1%  less  than  the  sus- 


165 

pended  truss  of  a  cantilever  bridge. 
The  empiric  formula  for  the  latter  may 
then  be  adapted  to  the  ordinary  truss 
*by  simply  reducing  the  weight-factor 
by  the  above  percentage,  giving 

T=.  00051  (T+F  +  LL)l. 
This  yields  T=  oo  for 


.00051 

It  thus  appears  that  the  limiting. 
length  for  a  simple  truss  is  about  three 
times  the  longest  span  yet  attempted. 

ART.  28 

MAXIMUM  PRACTICABLE  SPAN  FOR 
CANTILEVERS 

The  theoretical  maximum  span  estab- 
lished in  the  preceding  article  is  the 
limiting  span  which  may  be  approached 
by  increasing  the  sections  of  the  truss- 
members  indefinitely.  It  is  evident, 
however,  that  long  before  that  span  is 
reached,  the  required  cross-sections  will 
become  too  great  for  actual  construction. 


166 

'The  longest  span  at  which  the  cross- 
gections  of  the  members  will  not  exceed 
an  assigned  maximum  value,  determined 
by  the  limitations  of  design,  fabrication, 
transportation  or  erection,  will  be  termed 
the  maximum  practicable  span. 

In  the  three  cantilever  designs  exe- 
cuted above,  viz. 

L=1000,     1500,     2000ft., 

the  maximum  required  section  is  found 
in  the  lower  chord  of  the  anchor  arm 
and  amounts  to 


1302,     2338sq.in. 

It  will  be  observed  that  these  cross- 
sections  are  almost  exactly  proportional 
to  the  squares  of  the  respective  channel 
.spans.  Considering  also  that  the  sec- 
tion must  vary  with  the  live-load  for 
which  the  structure  is  designed,  we  may 
write  the  proportion 


Substituting    the  values    of    Amax,  LL 
&nd    L    from    the    above    designs,    and 


167 

solving  for  the  unknown  coefficient,  we 
find 

fc  =  .031,     .032,     .032, 
so    that    the    above    formula    becomes 
Amax=.032(LL)L2,    ...     (1) 

where  L  is  supposed  given  in  1000  ft. 
units. 

Hence  the  maximum  practicable  span 
for  a  cantilever  is  given  by 


where  Amax  is  the  greatest  practicable 
cross-section  (in  sq.  in.)  and  LL  is  the 
assumed  live-load  (in  Ibs.  p.l.f.). 

Value    of   Amax.     The    largest    cross- 
sections  ever  fabricated  are  the  following : 

Queensboro 1120  sq.in. 

Quebec 843 

Beaver 639 

Kansas  City  (Truss)  ...  485 

St.  Louis  (Truss) 441 

Monongahela 348 

Thebes 317 

Memphis 228 


168 

All  of  the  above  chord-sections  are 
of  the  multiple  rib  type.  The  number 
of  ribs  composing  the  section  never 
exceeds  four,  that  being  the  number  used 
in  the  Quebec,  Queensboro,  Thebes  and 
Memphis  Bridges.  Any  larger  number 
of  ribs  would  make  the  action  of  the 
whole  number  as  a  unit  extremely  prob- 
lematic; and,  in  the  light  of  recent 
experience,  no  conservative  engineer 
would  propose  such  a  section. 

The  greatest  depth  of  rib  is  5'6i" 
occurring  in  the  Beaver  Bridge,  followed 
by  a  depth  of  4'6i"  in  the  Quebec  and 
St.  Louis  Bridges.  In  LindenthaPs  de- 
sign for  the  Hell  Gate  Arch  (977'6" 
span),  a  10  ft.  depth  of  rib  is  proposed. 
This  is  so  far  in  advance  of  any  previous 
design,  and  involves  so  difficult  a 
problem  of  adequate  stiffening  and 
bracing,  besides  the  difficulties  of  fabrica- 
tion, that  it  may  well  be  taken  as  the 
extreme  limit  for  practicable  depth  of 
rib. 

The  greatest  thickness  of  rib  is  5f" 
in  the  Queensboro  Bridge,  followed  by 


169 

4^";  4J",  and  3J"  in  the  Monongahela, 
Hell  Gate  and  Quebec  Bridges,  respec- 
tively. On  account  of  the  extreme  dif- 
ficulty of  riveting  through  so  great  a 
thickness,  it  is  hardly  probable  that  any 
greater  thickness  than  the  above,  or 
say  6"  at  the  most,  will  ever  be  used. 
Combining  the  above  limitations,  we 
find  that  the  greatest  practicable  chord- 
section  would  consist  of  4  ribs,  10  ft. 
deep  and  6  in.  thick.  Adding  the  largest 
angles  obtainable  for  the  flanges,  the 
total  area  will  be,  in  round  numbers, 

Amax  =  3000  sq.in. 

With  the  necessary  diaphragms  and 
lacing,  such  a  member  would  weigh  over 
7  tons  per  linear  foot. 

This  value  of  Amax  is  nearly  three 
times  the  cross-section  of  the  largest 
member  ever  fabricated  (1120  sq.in.  in 
the  Queensboro  Bridge)  and  over  twice 
the  largest  section  to  be  used  in  the 
Hell  Gate  Arch  (1437  sq.  in.).  A  mem- 
ber of  2300  sq.in.  occurs  in  the  plans 
for  the  Hudson  River  Bridge  of  2160  ft. 


170 

span  designed  by  the  Union  Bridge 
Company  in  1893,  and  a  slightly  larger 
cross-section  (2338  sq.in.)  is  found  nec- 
essary in  the  writer's  design  of  a  2000 
ft.  cantilever  bridge.  But  the  above 
sectional  area  of  3000  sq.in.  is  far  in 
excess  of  any  chord  section  ever  pro- 
posed. 

Value  of  'Lmax.  Substituting  4max  =  3000 
in  eq.  (2)  above,  we  find  the  following 
values  of  the  maximum  span  for  differ- 
ent assumed  live  loads: 

For 


LL=  10,000  Ibs.  p.l.f.         £max  =  3060  ft. 
LL  =  15,000  Ibs.  p.l.f.          Lmax  =  2500  ft. 

LL  =  20,000  Ibs.  p.l.f.  Anax^2160  ft' 


As  it  could  hardly  be  considered  practical 
to  design  a  cantilever  bridge  of  the 
magnitude  under  consideration  for  a 
smaller  live  load  than  about  10,000  Ibs. 
per  linear  foot,  we  conclude  that  the 
maximum  practical  span  for  the  cantilever 
type  ranges  from  about  2000  to  3000  ft., 
depending  upon  the  assumed  live  load. 
Compare  these  with  the  corresponding 


171 

values  established  above  for  the  sus- 
pension bridge ,  viz., 

Zmax  =  3500to4900ft., 

indicating  the  greater  suitability  of  the 
suspension  type  to  extreme  long-span 
construction. 

ART.  29 

EMPIRIC  FORMULA  FOR  COST  OF 
CANTILEVER  BRIDGES 

As  in  the  case  of  suspension  bridges, 
the  expression  for  the  cost  of  any  span 
(L)  will  be  assumed  of  the  general  form: 

C  =  aL  +  6L2  +  cL3.     ...     (1) 

Since  we  have  but  three  values  for  C 
determined  by  actual  design,  the  for- 
mula is  limited  to  an  equal  number  of 
terms. 

From  the  results  of  the  preceding 
estimates,  we  have 

C  =  $4,905,000       for  L  =  1000  ft. 
C=  10,570,000  L=  1500  ft. 

C  =  22,125,000  L  =  2000  ft. 


172 

Substituting  these  values  in  eq.  (1),  the 
unknown  coefficients  are  determined, 
giving 

C=6350L-5.25  L2-f.0038L3,      (2) 

as  the  general  cost-formula  for  cantilever 
bridges.  This  gives  the  cost  of  steel- 
work and  substructure  for  an  assumed 
live  load  of  18000  Ibs.  per  linear  foot. 
For  any  other  loading,  the  cost  may  be 
taken  as  varying  in  proportion. 

ART.  30 
ECONOMIC  SPAN  FOR  CANTILEVERS 

As  established  in  the  preceding  article, 
the  cost  of  a  cantilever  bridge,  includ- 
ing steelwork  and  substructure,  is  given 
by  the  expression 


(1) 

Assuming  the  same  cost  of  approaches, 
volume  of  traffic,  life  of  steelwork, 
expense  of  maintenance  and  rate  of 
interest  as  for  the  suspension  type,  the 
limiting  economic  span  for  the  canti- 


173 

lever  will  be  defined  by  the  same  total 
cost  as  in  the  case  of  the  suspension 
bridge,  viz., 

C  =  $54,000,000. 

As  shown  in  Art,  19,  this  is  the  greatest 
expenditure  for  a  long-span  bridge, 
exclusive  of  approaches  and  accessories, 
that  is  warranted  by  the  maximum  traffic 
returns  to  be  reasonably  expected.  Sub- 
stituting this  value  in  eq.  (1)  and  solving 
we  find 

L  =  2700  ft. 

as  the  maximum  economic  span  for 
cantilevers. 

Hence,  the  greatest  span  for  which 
the  cantilever  type  may  be  profitably 
employed  is  2700  ft.  or  less,  depending 
upon  the  probable  maximum  traffic 
returns. 


174 


CHAPTER  VIII 
FINAL  COMPARISONS  AND  CONCLUSIONS 

ART.  31 

COSTS  OF  SUSPENSION  BRIDGES  AND 
CANTILEVERS 

In  the  accompanying  table  are  given 
the  costs  for  various  spans  of  suspension 
bridges  and  cantilevers  as  determined 
by  the  respective  empiric  formulae.  The 
following  relations  may  be  gleaned  from 
the  table : 

1.  The  cantilever  is  cheaper  than  the 
suspension  type  at  a  span  of  1500  ft.  or 
less.     The   suspension   is    cheaper   than 
the  cantilever  type  at  a  span  of  1750  ft. 
or  more. 

2.  The   cost   per   foot   of   length   for 
suspension  bridges  is  a  minimum  for  a 
span   of   about    1000   ft.,    indicating   a 
rapid  decrease  of  economy  in  the  use 
of  the  type  for  shorter  spans. 


175 


COStS   OF   SUSPENSION   BRIDGES   AND 

CANTILEVERS, 
for  LL  =  18,000  Ibs.  p.l.f. 


T 

1 

Suspension  Bridges. 

Cantilever  Bridges. 

Total  Cost 
=  C 

Cost 
per 
Foot. 
=  C 
+  21 

•1- 
0 

II 

^ 

Total  Cost 
=  C 

Cost 
per 
Foot. 
=  C 
+  1.81 

£> 
•1- 
O 
II 
N 

250 
500 
750 
1000 
1250 
1500 

$ 
2,023,000 
3,758,000 
5,395,000 
7,130,000 
9,140,000 
11,645,000* 

$ 
4,040 
3,760 
3,595 
3,565 
3,655 
3,880 

32.3 
15.0 
9.6 
7.1 
5.8 
5.2 

4.5 
4.7 

4.7 
4.8 
4.9 
5.2 
5.5 
5.8 
6.1 
6.4 

$ 

1,343,000 
2,288,000 
3,410,000 
4,-905,000* 
7,035,000 
-  10,570,000* 

$ 

2,980 
2,540 
2,525 
2,725 
3,130 
3,910 

21.6 
9.2 
6.1 
4.9 
4.5 
4.7 

5.0 
5.5 
6.1 
6.8 
7.5 
8.3 
9.1 
10.0 
10.7 
11.5 

1750 
2000 
2250 
2500 
2750 
3000 
3250 
3500 
3750 
4000 

14,130,000 
18,720,000 
23,760,000* 
29,950,000 
37,390,000 
46,785,000* 
57,710,000 
71,050,000 
85,780,000 
103,200,000 

4,040 
4,680 
5,280 
5,990 
6,790 
7,780 
8,870 
10,160 
11,450 
12,900 

15,370,000 
22,125,000* 
30,990,000 
42,570,000 
56,910,000 
74,650,000 
95,740,000 
121,120,000 
150,710,000 
184,900,000 

4,880 
6,150 
7,640 
9,450 
11,500 
13,850 
16,360 
19,240 
22,300 
25,680 

C=8900Z-3.77Z2+0.002Z3      C 

*  Values  obtained  by  aptual  design.  Other  values 
interpolated  or  extrapolated  by  aid  of  empiric  formulae 
given  below. 

3.  The  cost  per  foot  of  length  for 
cantilevers  is  a  minimum  for  a  span  of 
about  600  ft.,  indicating  a  rapid  decrease 
of  economy  in  the  use  of  the  type  for 
shorter  spans. 


176 

4.  Between   the    limits    of    1500    and 
3000  ft.  for  suspension  bridges,  and  of 
1000  and   1750  ft.  for  cantilevers,  the 
value  of  K(  =  C  +  l2)  remains  fairly  con- 
stant.    Hence,    for    all    normal    spans, 
the  cost  of  either  type  may  be  estimated 
as  varying  approximately  with  the  square 
of  the  span.     Within  the  above  ranges,  as 
an  average  value, 

C  =  4.7l2  for  suspension  bridges 
and 

C  =  4.8  L2  for  cantilevers. 

5.  The  value  of  K  for  the  suspension 
bridges  is  a  minimum  for  a  span  of  about 
1800  ft.,  indicating  that  that  is  the  span 
for  which  the  suspension  type  is  economi- 
cally best  adapted. 

6.  The  value  of  K  for  the  cantilevers 
Is  a  minimum  for  a  span  of  about  1250 
ft.,  indicating  that  that  is  the  span  for 
which  the  cantilever  type  is  economically 
best  adapted. 

7.  The    limiting    economic    span,    i.e. 
the  greatest  span  for  profitable  erection, 
defined    by    C  =  $54,000,000,    is    shown 


177 

by  the  table  to  be  about  3200  ft.  for 
the  suspension  type  and  about  2700  ft. 
for  the  cantilever  type. 

The  tabulated  costs,  where  they  lie 
outside  of  the  spans  actually  designed, 
are  subject  to  the  inherent  errors  of  any 
method  of  extrapolation;  but  the  above 
results  are  sufficiently  accurate  for  the 
purposes  of  this  investigation. 

ART.  32 
SPAN  OF  EQUAL  COST 

PLOTTING  the  costs  for  the  three  sus- 
pension spans  designed  above,  a  smooth 
curve  passing  through  the  three  points 
and  the  origin  constitutes  a  cost-graph 
for  suspension  bridges.  In  the  same 
manner,  the  graph  representing  the  costs 
for  different  cantilever  spans  is  con- 
structed. The  point  where  the  two 
curves  intersect  marks  the  span  of  equal 
cost  for  the  two  types  of  construction > 
and  is  found  at 

1=1670  ft. 


178 

Below  this  span,  the  cantilever  bridge 
is  cheaper;  above  this  span,  the  sus- 
pension bridge  exhibits  the  greater  econ- 
omy. As  this  value  lies  within  the 
range  of  spans  actually  designed  for 
each  bridge,  i.e.,  between  the  known 
points  on  each  graph,  the  error  of  the 
above  method,  involved  in  extending 
the  results  of  individual  designs  to  other 
spans,  is  negligible. 

The  analytical  equivalent  of  the  above 
process  consists  in  comparing  the  cost- 
formula  for  the  two  types  of  bridges. 
The  cost  of  a  suspension  bridge,  designed 
for  a  live-load  of  18,000  Ibs.  per  linear 
foot,  as  established  in  Art.  19,  is  given  by 

C=890(M-3.77P  +.0020P,        (1) 

and  that  of  a  cantilever  bridge  for  the 
same  loading,  as  established  in  Art.  39, 


(2) 


where  I  denotes  the  total  channel  span. 
Equating  expressions   (1)   and   (2),  and 


179 


COST  GRAPH 


^ 


FOR 

SUSPENS,ION|BRI|DGES 


AND 
iLEl 


VERS_ 


1-jJI 

0  /      oi 

u    /          of: 

1  /         m.r1 


± 


^ 


Z^ 


250  500  750  1000  12501500  1750  2000  2250  25002750  3000  32503500  3750 
SPAN  (IN  FT.) 


180 

solving,  we  find,  for  the  span  of  equal 
cost, 

1  =  1670  ft. 

exactly  as  before. 

The  above  comparison  is  somewhat 
unfair  to  the  suspension  type,  as  the  side- 
spans  in  the  above  designs  were  0.5Z  in 
the  suspension  bridges  and  only  OAl 
in  the  cantilevers.  Assuming,  therefore, 
that  steel  viaduct  approaches  are  added 
to  the  cantilever  bridges  to  make  up 
the  difference  in  total  length,  and  esti- 
mating the  cost  of  such  viaducts  at 
$1000  per  linear  foot/  the  expression 
(2)  becomes  modified  to 

C  =  6550/-5.25Z2-f.0038Z3.       .     (3) 

Equating  this  to  expression  (1)  and 
solving  for  the  span  of  equal  cost,  we 
find 

1=  1626  ft,, 

somewhat  less  than  the  value  established 
above.  If  the  comparison  of  costs  had 

1  This  is  the  price  assumed  in  a  similar  case 
by  the  U.  S.  Board  of  Engineers  in  1894. 


181 

been  made  between  bridges  of  equal 
total  length  instead  of  between  bridges 
of  equal  channel  span,  the  result  would 
have  been  still  more  favorable  to  the 
suspension  bridge,  reducing  the  critical 
span  to  about 

J»  1500  ft, 

Neglecting  these  differences  in  favor 
of  the  suspension  type,  we  conclude  that 
^  =  1670  ft.  is  the  extreme  upper  limit  of 
spans  at  which  the  cantilever  can  com- 
pete with  the  suspension  bridge,  when 
economy  is  the  sole  criterion. 

ART.  33 
SUMMARY 

The  results  of  the  preceding  investiga- 
tions may  be  summarized  as  follows: 

1.  Maximum  Span  for  a  Cable.  The 
.greatest  span  theoretically  possible  for 
a  steel  cable  of  any  cross -sect  ion  is 
65,520  ft.  based  on  the  ultimate  resistance; 
21,840  ft.  based  on  a  safe  working- 
stress  of  60,000  Ibs.  per  sq.in.;  15,100  ft* 


182 

if  the  rise  is  restricted  to  the  economic 
ratio  of  one-eighth  the  span;  and  14,700 
ft.  if  the  weight  of  cable-wrapping  and 
fastenings  is  taken  into  consideration. 

2.  Maximum     Span    for     Suspension 
Bridges.     The   last   value,   14,700   ft.,  is 
also    the    maximum    span    theoretically 
possible  for  a  stiffened  suspension  bridge. 
The   greatest   practicable   span,   defined 
by  a  maximum  section  of  16  cables  of  24 
inches   diameter   with  a  minimum  live- 
load   of    10,000   Ibs.   per  linear  foot,  is 
4300  ft. 

3.  Economic     Span     for     Suspension 
Bridges.     The  greatest  suspension  span, 
for  which  the  necessary  outlay  would  be 
warranted  by  the  probable  traffic  returns 
is  3170  ft. 

4.  Maximum     Span     for     Cantilever 
Bridges.     The  greatest  span  theoretically 
possible  for  a  cantilever  bridge  is  5600 
ft.     In    this   maximum   span,   the   sus- 
pended span  will  be  1850  ft.,  the  canti- 
lever arms  1875  ft.,  and  the  anchor  arms 
2760  ft.     The  practical  limit  for  canti- 
levers,  denned   by   a   maximum   chord- 


183 

section  of  3000  sq.in.,  with  a  minimum 
live-load  of  10,000  Ibs.  per  linear  foot, 
is  3060  ft. 

5.  Maximum    Span   for    Truss.    The 
greatest  span  theoretically  possible  for 
a  simple  truss  is  1960  ft. 

6.  Economic      Span     for      Cantilever 
Bridges.     The  maximum  economic  span 
for  cantilevers,  denned  by  the  condition 
of  zero  net   profit  on  the  investment,  is 
2700  ft. 

7.  Span  of  Equal  Cost.     The   critical 
span    at    which    the    suspension    bridge 
becomes    economically    superior    to    the 
cantilever  bridge  is  1670  ft. 

Summary:  s  B  c  •% 

Theoretical  max.  span. .  14,700         5,600 

Practical  max.  span 4,900         3,060 

Max.  economic  span.  .  .  .  3,170         2,700 

Span  of  equal  cost 1,670 

ART,  34 
CONCLUSIONS 

In  the  foregoing  designs,  special  care 
was  taken  to  proportion  the  depths  of 
truss  in  both  types  for  equal  and  ample 


184 

rigidity ,  so  that  the  single  inherent 
advantage  claimed  for  cantilevers,  viz. 
greater  stiffness  for  railway  traffic,  is 
eliminated  from  consideration.  Con- 
sequently no  advantage  remains  to  the 
cantilever  type  above  the  limiting  span 
of  1670  ft.  The  suspension  bridge, 
on  the  other  hand,  is  universally  ad- 
mitted to  possess  greater  aesthetic  qual- 
ifications; and,  for  a  long-span  city 
structure,  this  is  a  factor  of  decisive 
importance.  For  this  reason  alone  the 
above  value  for  the  span  of  equal  cost 
should  be  considerably  reduced  in  favor 
of  the  suspension  type,  to  obtain  the 
"span  of  equal  merit." 

The  preceding  investigations  have  been 
restricted  to  designs  for  heavy  railway 
traffic.  For  highway  bridges,  a  rela- 
tively lighter  stiffening  truss  may  be 
used  in  the  suspension  type,  thereby 
causing  a  considerable  reduction  in  the 
span  of  equal  cost. 

Confining  our  attention  to  economic 
considerations,  our  final  conclusions  may 
be  stated  as  follows: 


185 

1.  The    range    of   economic    usefulness 
for    cantilevers    extends  from    the    upper 
limit  for  the  truss  or  arch  to  a  span  of 
1670  ft.     Beyond  this  value ,  the  cantilever 
would  be  more  costly  than  the  suspension 
type,  although    yielding  a  probable  profit 
on  the  investment  up  to  a  span  of  2700  ft. 

2.  The    range    of   economic    usefulness 
for    suspension    bridges    begins    at    1670 
ft.  (or  less  in  the  case  of  highway  bridges) 
and  extends  to  the  upper  economic  limit 
of  3170  ft.     Above  this  limit,  the  construc- 
tion    of    suspension    bridges     would    be 
practically  feasible,  but  not  as  a  profitable 
investment,    up    to    an    extreme    limit    of 
4900ft. 


Vita 


Born  June  11,  1886. 

B.  S.  (Summa  cum  laude) , 
College  of  the  City  of  New  York, 
1906. 

A.  M.9  C.  E.,  Columbia  Uni- 
versity, 1909.  Ph.  D.,  1911. 

Fellow  in  Applied  Mathe- 
matics, College  of  the  City  of 
New  York,  1906-1909.  Tutor  in 
Surveying  1909-1910.  James 
Scholar  in  Applied  Science, 
Columbia  University,  1907-1909. 
University  Scholar  in  Engineer- 
ing, 1909-1910.  Instructor  in 
Applied  Physics,  Stuyvesant  Eve- 
ning High  School,  1909-1910. 

Instructor  in  Civil  Engineer- 
ing, University  of  Idaho,  1910-1911. 
Assistant  Professor,  1911. 


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SCIENTIFIC  PUBLICATIONS.  lS 


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20  D.  VAtt   NOSTRAttD 


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^OBLIGATIONS.  21 


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HERRMANN,      G.        The      Graphical      Statics      of 

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SCIENTIFIC   PUBLICATIONS.  27 


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HUBRARD,   E.      The    Utilization   of   Wood-waste. 

A  Complete  Account  of  the  Most  Advantageous 
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HUMBER,  W.,  C.E.  A  Handy  Book  for  the  Cal- 
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plement   net,  $1 . 25 

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,, ,,,,,,,,,,,,,...,.,,,...,.., net,  $2 .50 


SCIENTIFIC  PUBLICATIONS.  29 


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KENNEDY,  R.  Modern  Engines  and  Power  Gen- 
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SCIENTIFIC   PUBLICATIONS.  33 


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34  D.    VAN    NOSTRAND   COMPANY'S 


and  other  Properties  of  Materials  used  in  Con- 
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KLEIN,  J.  F.  Design  of  a  High-speed  Steam- 
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KL.EINHANS,    F.     B.       Boiler     Construction.       A 

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KNIGHT,     A.     M.,     Lieut.-Com.,     U.S.N.       Modern 

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Second  Edition,   revised    net,  $6.00 

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KOESTER,  F.     Steam-Electric  Power  Plants  and 

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ROLLER,  T.     The  Utilization  of  Waste  Products. 

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Cosmetics.     A  Handbook  of  the  Manufacture, 

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KRAUCH,  C.,  Dr.     Testing  of  Chemical  Reagents 

for  Purity.  Authorized  translation  of  the 
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SCIENTIFIC  PUBLICATIONS.  35 


Dupre.  With  additions  and  emendations  by 
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LAMBERT,  T.     Lead,  and  its  Compounds.        With 

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LAMBORN,  L.  L.  Cottonseed  Products.  A  Man- 
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With  Tables,  figures,  full-page  plates,  and  a 
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Modern    Soaps,    Candles,    and    Glycerin.         A 

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LAMPRECHT,    R.         Recovery    Work    After    Pit 

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LARRABEE,    C.    S.         Cipher    and    Secret    Letter 

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German  edition,  by  M.  M.  Pattison  Muir,  M.  A. 
12mo,  cloth,  illustrated $2.00 

LATTA,  M.  N.  Handbook  of  American  Gas- 
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LEASK,  A.  R.        Breakdows  at   Sea  and   How  to 

Repair  Them.  With  89  illustrations.  Second 
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36  D.    VAN    NOSTRAND   COMPANY'S 


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LEFEVRE,    L.       Architectural    Pottery:    Bricks, 

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LEHNER,  S.  Ink  Manufacture:  including  Writ- 
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LEMSTROM,  Dr.     Electricity  in  Agriculture  and 

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LIVERMORE,  V.  P.,  and  WILLIAMS,  J.     How  to 

Become  a  Competent  Motorman.  Being  a 
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LOBBEN,  P.,  M.E.      Machinists'  and   Draftsmen's 

Handbook,  containing  Tables,  Rules,  and  For- 
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SCIENTIFIC  PUBLICATIONS.  S7 


LOCKE,  A.  G.  and  C.  G.     A  Practical  Treatise  on 

the  Manufacture  of  Sulphuric  Acid.  With  77 
constructive  plates,  drawn  to  scale  measure- 
ments, and  other  illustrations.  Royal  8vo, 
cloth  .................................  $10.00 

LOCKWOOD,  T.  D.     Electricity,  Magnetism,  and 

Electro-telegraphy.  A  Practical  Guide  for 
Students,  Operators,  and  Inspectors.  8vo, 
cloth.  Third  Edition  ..................  $2.50 

——Electrical     Measurement    and    the    Galvano- 

meter: its  Construction  and  Uses.  Second  Edi- 
tion. 32  illustrations.  12mo,  cloth  ----  $1.50 

LODGE,  O.  J.     Elementary  Mechanics,  including* 

Hydrostatics  and  Pneumatics.  Revised  Edi- 
tion. 12mo,  cloth  .....................  $1.50 

-  Signalling     Across     Space,     Without     Wires: 

being  a  description  of  the  work  of  Hertz  and 
his  successors.  With  numerous  diagrams  and 
half-tone  cuts,  and  additional  remarks  con- 
cerning the  application  to  Telegraphy  and 
later  developments.  Third  Edition.  8vo,  cloth, 
illustrated  ........................  net,  $2.00 

LORD,  R.  T.     Decorative  and  Fancy  Fabrics..   A 

Valuable  Book  with  designs  and  illustrations 
for  manufacturers  and  designers  of  Carpets, 
Damask,  Dress  and  all  Textile  Fabrics.  8vo, 
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LORING,    A.    E.      A.    Handbook    of    the    Electro- 

magnetic Telegraph.  16mo,  cloth,  boards. 
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LUCE,    S.   B.    (Com.,   U.S.N.)      Text  -book   of   Sea- 

manship. The  Equipping  and  Handling  of 
Vessels  under  Sail  or  Steam.  For  the  use  of 
the  U.  S.  Naval  Academy.  Revised  and  en- 
larged edition,  by  Lieut.  Wm.  S.  Benson.  8vo, 


rge 
oth, 


.  .     . 

cloth,    illustrated     .....................  $10.00 

LUCRE,   C.  E.      Gas   Engine   Design.      With    fig- 

ures and  diagrams.  Second  Edition,  revised. 
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-  Power  Plants:   their  Design,  Efficiency,  and 

Power  Costs.     2  vols  ................  In  Press. 

Power   Plant    Papers..    Form   I.      The    Steam 

Power  Plant.     Pamphlet  (8x13)    .....  net,  $1.50 
LUNGE,  G.,  Ph.D.     Coal-tar  and  Ammonia:  being 

the  third  and  enlarged  edition  of  "A  Treatise 
on  the  Distillation  of  Coal-tar  and  Ammoni- 
acal  Liquor,"  with  numerous  tables,  figures 
and  diagrams.  Thick  8vo,  cloth,  illustrated. 
...................................  net,  $15.00 


38  D.    VAN    KOSTRAND   COMPANY^ 


A   Theoretical  and  Practical  Treatise  on  the 

Manufacture  of  Sulphuric  Acid  and  Alkali 
with  the  Collateral  Branches.  . 

Vol.     I*       Sulphuric      Acid.       In    two      parts,    not 

sold  separately.  Second  Edition,  revised  and 
enlarged.  342  illus.  8vo,  cloth $15. 00 

Vol.     II.  '    Salt      Cake,    Hydrochloric      Acid      and 

Leblanc  Soda.  Second  Edition,  revised  and 
enlarged.  8vo,  cloth  $15 . 00 

Vol.     III.       Ammonia     Soda,     and     various     other 

processes  of  Alkali-making,  and  the  prepara- 
tion of  Alkalis,  Chlorine  and  Chlorates,  by 
Electrolysis.  8vo,  cloth.  New  Edition,  1896. 
k  ;••'.; $15 .  oo 

and  HURTER,  F.     The  Alkali  Maker's  Hand- 

book.  Tables  and  Analytical  Methods  for 
Manufacturers  of  Sulphuric  Acid,  Nitric  Acid, 
Soda,  Potash  and  Ammonia.  Second  Edition. 
12m0,  cloth  ...$3.00 

L.UPTON,   A.,   PARR,   G.   D.   A.,  and   PERKIN,   H. 

Electricity  as  Applied  to  Mining.  With  tables, 
diagrams  and  folding  plates.  Second  Edition, 
revised  and  enlarged.  8vo,  cloth,  illustrated. 
net,  $4.50 

LUQ,UER,  Lu  M.,  Ph.D.  (Columbia  Univ.).  Min- 
erals in  Rock  Sections.  The  Practical  Method 
o£  Identifying  Minerals  in  Rock  Sections  with 
the  Microscope.  Especially  arranged  for  Stu- 
dents in  Technical  and  Scientific  Schools.  Re- 
vised Edition.  8vo,  cloth,  illustrated,  net,  $1.50 

MACKIE,    John.      How   to    Make    a    Woolen    Mill 

Pay.     8 vo,  cloth net,  $2 . 00 

MACKROW,  C.  The  Naval  Architect's  and  Ship- 
builder's Pocket-book  of  Formulae,  Rules,  and 
Tables;  and  Engineers'  and  Surveyors'  Handy 
Book  o_f  Reference.  Ninth  Edition.  16mo, 
limp  leather,  illustrated  $5.00 

MAGUIRE,    E.,    Capt.,    U.S.A.       The    Attack    and 

Defense  of  Coast  Fortifications.  With  maps 
and  numerous  illustrations.  8vo,  cloth,  $2.50 

Wm.    R.      Domestic    Sanitary    Drainage    and 

Plumbing  Lectures  on  Practical  Sanitation. 
332  illustrations.  8vo  $4.00 

^f  AUKS,  E.  C.  R.     Notes  on  the  Construction  of 

Cranes  and  Lifting  Machinery.  With  numer- 
ous diagrams  and  figures.  New  and  enlarged 
edition.  12mo,  cloth  net,  $1.50 


SCIENTIFIC  PUBLICATIONS.  39 


—  Votes   on  the   Construction   and  Working   of 

Pumps.  With  figures,  diagrams  and  engrav- 
ings. 12mo,  cloth,  illustrated  net,  $1.50 

G.     C.       Hydraulic     Power    Engineering.       A 

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ery. With  over  200  diagrams  and  tables.  8vo, 
cloth,  illustrated  $3.50 

MARKHAM,  E.  R.     Steel  Worker,  The  American. 

A  twenty-five  years  experience  in  the  selection, 
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of  various  kinds  and  grades  of  steel.  8vo, 
cloth.  Illus.  Second  Edition  $2.50 

MARSH,  C.  F.,  and  DUNN,  W.  Reinforced  Con- 
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512  figures  and  diagrams.  Third  Edition,  re- 
vised and  enlarged.  4to,  cloth,  illus.,  net,  $7.00 

MAURICE,    WM.       Electric    Blasting    Apparatus 

and  Explosives:  with  Special  Reference  to 
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MAVER,    W.       American     Telegraphy:     Systems, 

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MAYER,  A.  M.,  Prof.     Lecture  Notes  on  Physics. 

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McCUL,L,OUGH,  R.  S.,  Prof.     Elementary  Treatise 

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McINTOSH,  J.  G.  Technology  of  Sugar.  A  Prac- 
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diagrams  and  tables.  8vo,  cloth,  illustrated. 
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Industrial    Alcohol.      A   Practical    Manual    on 

the  Production  and  Use  of  Alcohol  for  Indus- 
trial Purposes  and  for  Use  as  a  Heating  Agent, 
as  an  Illuminant  and  as  a  Source  of  Motive 
Power.  With  plans  and  engravings.  8vo, 
cloth,  ill.  252  pp.,  London,  1907 net,  $3.0O 

Manufacture  of  Varnishes  and  Kindred  In- 
dustries, Based  on  and  including  the  "Drying 
Oils  and  Varnishes,"  of  Ach.  Livache.  Volume 
I.  Oil  Crushing,  Refining  and  Boiling,  Manu- 
facture of  Linoleum,  Printing  and  Lithograph- 
ic Inks,  and  India-rubber  Substitutes.  Second 


40  D.   VAN    NOSTRAND   COMPANY'S 


greatly  enlarged  English  Edition.     8vo,  cloth, 

illustrated     net,     $3.50 

(To   be  complete  in   three  volumes.) 

McMECHEN,  F.  L.     Tests  for  Ores,  Minerals  and 

Metals  of  Commercial  Value.  8vo,  cloth,  illus- 
trated   In  Press. 

MCNEIL.L,,  B.     McNeill's  Code.     Arranged  to  meet 

the  requirements  of  Mining,  Metallurgical  and 
Civil  Engineers,  Directors  of  Mining,  Smelting 
and  other  Companies,  Bankers,  Stock  and 
Share  Brokers,  Solicitors,  Accountants,  Finan- 
ciers and  General  Merchants.  Safety  and  Se- 
crecy. 8vo,  cloth  $6.00 

McPHERSON,  J.  A.,  A.  M.  Inst.  C.  E.  Water- 
works Distribution.  A  practical  guide  to  the 
laying  out  of  systems  of  distributing  mains 
for  the  supply  of  water  to  cities  and  towns. 
With  tables,  folding  plates,  and  numerous  full- 
page  diagrams.  8vo,  cloth,  illustrated,  $2.50 

MEL.ICK,  C.  W.,  Prof.     Dairy  Laboratory  Guide. 

In    Press. 

MERCK,    E.      Chemical    Reagents;    Their    Purity 

and  Tests,   250   pp net,     $1.50 

MERRITT,  Wm.  H.     Field  Testing  for  Gold  and 

Silver.  A  Practical  Manual  for  Prospectors 
and  Miners.  With  numerous  half-tone  cuts, 
figures  and  tables.  16mo,  limp  leather,  illus- 
trated    $1.50 

METAL  TURNING.  By  a  Foreman  Pattern- 
maker. Illustrated  with  81  engravings.  12mo, 
cloth $1.50 

MICHELL,  S.      Mine  Drainage;  being  a  Complete 

Practical  Treatise  on  Direct-acting  Under- 
ground Steam  Pumping  Machinery.  Contain- 
ing many  folding  plates,  diagrams  and  tables. 
Second  Edition,  rewritten  and  enlarged.  Thick 
8vo,  cloth,  illustrated  $10.00, 

MIERZINSKI,  S.,  Dr.     Waterproofing  of  Fabrics. 

Translated  from  the  German  by  Arthur  Mor- 
ris and  Herbert  Robson.  With  diagrams  and 
figures.  8vo,  cloth,  illustrated  ....  net,  $2.50 

MILLER,  E.  H.    (Columbia   Univ.).     Quantitative 

Analysis  for  Mining  Engineers.  8vo,  cloth, 
Second  Ed.  Revised  net,  $1.50 

MIL.ROY,  M.  E.  W.  Home  Lace-making;  a  Hand- 
book for  Teachers  and  Pupils.  With  plates 
and  diagrams.  12mo,  cloth,  illustrated. 
...,., net,  $1,00 


SCIENTIFIC   PUBLICATIONS.  41 


MINIFIE,  W.  Mechanical  Drawing.  A  Text- 
book of  Geometrical  Drawing1  for  the  use  of 
Mechanics  and  Schools,  in  which  the  Defini- 
tions and  Rules  of  Geometry  are  familiarly 
explained;  the  Practical  Problems  are  '  ar- 
ranged from  the  most  simple  to  the  more  com- 
plex, and  in  their  description  technicalities 
are  avoided  as  much  as  possible.  With  illus- 
trations for  drawing  Plans,  Sections,  and  Ele- 
vations of  Railways  and  Machinery;  an  Intro- 
duction to  Isometrical  Drawing,  and  an  Essay 
on  Linear  Perspective  and  Shadows.  Illus- 
trated with  over  200  diagrams  eng-raved  on 
steel.  Tenth  Thousand,  revised.  With  an  Ap- 
pendix on  the  Theory  and  Application  of  Col- 
ors. 8vo,  cloth  $4.00 

Geometrical    Drawing.      Abridged    from    the 

Octavo  edition,  for  the  use  of  schools.  Illus- 
trated with  48  steel  plates.  Ninth  Edition. 
12m.o,  cloth  $2 . 00 

MODERN     METEOROLOGY.       A     Series     of     Six 

Lectures,  delivered  under  the  auspices  of  the 
Meteorological  Society  in  1870.  Illustrated. 
12mo,  cloth  $1.50 

MOORE,  E.   C.   S.      New  Tables  for  the   Complete 

Solution  of  Ganguillet  and  Kutter's  Formula 
for  the  flow  of  liquids  in  open  channels,  pipes, 
sewers  and  conduits.  In  two  parts.  Part  I, 
arranged  for  1080  inclinations  from  1  over  1 
to  1  over  21,120  for  fifteen  different  values  of 
(n).  Part  II,  for  use  with  all  other  values  of 
(n).  With  large  folding-  diagram.  8vo,  cloth, 
illustrated  net,  $5 . 00 

MOREING,    C.   A.,   and    NEAL,,   T.      New    General 

and  Mining  Telegraph  Code.  676  pages,  al- 
phabetically arranged.  For  the  use  of  mining 
companies,  mining  engineers,  stock  brokers, 
financial  agents,  and  trust  and  finance  com- 
panies. Eighth  Edition.  8vo,  cloth  ...$5.00 

MOSES,  A.  J.     The   Characters   of  Crystals.     An 

Introduction  to  Physical  Crystallography,  con- 
taining 321  illustrations  and  diagrams.  8vo. 
net,  $2.00 

and  PARSONS,  C.  It.  Elements  of  Mineral- 
ogy, Crystallography  and  Blowpipe  Analysis 
from  a  Practical  Standpoint.  Fourth  Enlarged 
Edition.  8vo,  cloth,  336  illustrations,  net,  $2.50 

MOSS,    S.    A.      Elements    of    Gas    Engine    Design. 

Reprint  of  a  Set  of  Notes  accompanying  a 
Course  of  Lectures  at  Cornell  University  in 
1902.  Second  Edition.  16mo,  cloth,  illustrated. 
(Va,n  Nostrand's  Science  Aeries)  $0.50 


42  D.   VAN    NOSTRAND   COMPANY'S 


The    Lay-out    of    Corliss    Valve    Gears.    (Van 

nostrand's  Science  Series.)  16mo,  cloth,  illus- 
trated   $0.50 

MULLIN,  J.  P.,  M.E.  Modern  Moulding:  and  Pat- 
tern-making. A  Practical  Treatise  upon  Pat- 
tern-shop and  Foundry  Work:  embracing  the 
Moulding  of  Pulleys,  Spur  Gears,  Worm  Gears, 
Balance-wheels,  Stationary  Engine  and  Loco- 
motive Cylinders,  Globe  Valves,  Tool  Work, 
Mining  Machinery,  Screw  Propellers,  Pattern- 
shop  Machinery,  and  the  latest  improvements 
in  English  and  American  Cupolas;  together 
with  a  large  collection  of  original  and  care- 
fully selected  Rules  and  Tables  for  every-day 
use  in  the  Drawing  Office,  Pattern-shop  and 
Foundry.  12mo,  cloth,  illustrated  $2.50 

MUNRO,    J.,    C.E.,    and    JAMIESON,    A.,    C.E.      A 

Pocket-book  of  Electrical  Rules  and  Tables 
for  the  us.e  of  Electricians  and  Engineers. 
Sixteenth  Edition,  revised  and  enlarged.  With 
numerous  diagrams.  -  Pocket  size.  Leather. 
$2 . 50 

MURPHY,  J.  G.,  M.E.     Practical  Mining.     A  Field 

Manual  for  Mining  Engineers.  With  Hints  for 
Investors  in  Mining  Properties.  16mo,  cloth. 
$1.00 

NAQ,UET,  A.     Legal  Chemistry.     A  Guide  to  the 

Detection  of  Poisons,  Falsification  of  Writings, 
Adulteration  of  Alimentary  and  Pharmaceuti- 
cal Substances,  Analysis  of  Ashes,  and  Exami- 
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plied to  Chemical  Jurisprudence,  for  the  use  of 
Chemists,  Physicians,  Lawyers,  Pharmacists 
and  Experts.  Translated,  with  additions,  in- 
cluding a  list  of  books  and  memoirs  on  Toxi- 
cology, etc.,  from  the  French,  by  J.  P.  Batter- 
shall,  Ph.D.,  with  a  preface  by  C.  F.  Chandler, 
Ph.D.,  M.D.,  LL.D.  12mo,  cloth  $2.00 

NASMITH,    J.      The    Student's    Cotton    Spinning. 

Third  Edition,  revised  and  enlarged.  8vo, 
cloth,  622  pages,  250  illustrations  $3.00 

NEUBERGER,  H.,  and  NOAL.HAT,  H.  Technol- 
ogy of  Petroleum.  The  Oil  Fields  of  the 
World:  their  History,  Geography  and  Geology. 
Annual  Production,  Prospection  and  Devel- 
opment; Oil-well  Drilling;  Transportation  of 
Petroleum  by  Land  and  Sea.  Storage  of  Pe- 
troleum. With  153  illustrations  and  25  plates. 
Translated  from  the  French  by  John  Geddes 
SVQ,  cloth,  illustrated,  net,  $10  00 


SCIENTIFIC  PUBLICATIONS.  43 


NEWALL,  J.  W.      Plain  Practical   Directions   for 

Drawing,  Sizing  and  Cutting  Bevel-gears, 
showing  how  the  Teeth  may  be  cut  in  a  Plain 
Milling  Machine  or  Gear  Cutter  so  as  to  give 
them  a  correct  shape  from  end  to  end;  and 
showing  how  to  get  out  all  particulars  for 
the  Workshop  without  making  any  Drawings. 
Including  a  Full  Set  of  Tables  of  Reference. 
Folding  plates.  8vo,  cloth  91.50 

NEWLANDS,    J.      The    Carpenters'    and    Joiners' 

Assistant:  being  a  Comprehensive  Treatise  on 
the  Selection,  Preparation  and  Strength  of  Ma- 
terials, and  the  Mechanical  Principles  of 
Framing,  with  their  application  in  Carpentry, 
Joinery  and  Hand-railing;  also,  a  Complete 
Treatise  on  Sines;  and  an  Illustrated  Glossary 
of  Terms  used  in  Architecture  and  Building. 
Illustrated.  Folio,  half  morocco  $15.00 

NIPHER,  P.  E.,  A.M.  Theory  of  Magnetic  Meas- 
urements, with  an  Appendix  on  the  Method  of 
Least  Squares.  12mo,  cloth  $1.00 

NISBET,  H.     Grammar  of  Textile  Design.     With 

many  diagrams  and  figures.  8vo,  cloth,  illus- 
trated. 276  pp.,  London,  1907  net,  $3.00 

NOLL,,    Augustus.      How    to    Wire    Buildings:    A 

Manual  of  the  Art  of  Interior  Wiring.  With 
many  illustrations.  Fourth  Edition.  8vo, 
cloth,  illustrated  $1.50 

NUGENT.  E.      Treatise   on   Optics;   or,  Light  and 

Sight  Theoretically  and  Practically  Treated, 
with  the  Application  to  Fine  Art  and  Indus- 
trial Pursuits.  With  103  illustrations.  12mo, 
cloth  $1.50 

O'CONNOR,  H.     The  Gas  Engineer's  Pocket-book. 

Comprising  Tables,  Notes  and  Memoranda  re- 
lating to  the  Manufacture,  Distribution  and 
Use  of  Coal-gas  and  the  Construction  of  Gas- 
works. Second  Edition,  revised.  12mo,  full 
leather,  gilt  edges  $3.50 

OLSEN,  J:   C.,   Prof.      Text-book   of   Quantitative 

Chemical  Analysis  by  Gravimetric,  Electro- 
lytic, Volumetric  and  Gasometric  Methods. 
With  Seventy-two  Laboratory  Exercises  giv- 
ing "the  Analysis  of  Pure  Salts,  Alloys,  Miner- 
als, and  Technical  Products.  With  numerous 
figures  and  diagrams.  Second  Edition,  re- 
vised. 8vo,  cloth  net,  $4.00 

OSBORN,   F.   C.      Tables   of   Moments   of   Inertia, 

and  Squares  of  Radii  of  Gyration;  supple- 
mented by  others  on  the  Ultimate  and  Safe 
Strength  of  Wrought-iron  Columns,  Safe 


44  D.   VAN    NOSTRAKD 


Strength  of  Timber  Beams,  and  Constants  for 
readily  obtaining  the  Shearing  Stresses,  Reac- 
tions and  Bending  Moments  in  Swing  Bridges. 
Fifth  Edition.  12mo,  leather  net,  $3.00 

OUDIN,    M.    A.      Standard    Polyphase    Apparatus 

and   Systems.      With   many   diagrams   and   fig- 
ures.      Fifth     Edition,     revised     and     enlarged. 
'Fully  illustrated.     8vo,  cloth,   370  pp.    ...$3.00 

PAL.AZ,  A.,  Sc.D.  A  Treatise  on  Industrial  Pho- 
tometry, with  special  application  to  Electric 
Lighting.  Authorized  translation  from  the 
French  by  George  W.  Patterson,  Jr.  Second 
Edition,  revised.  8vo,  cloth,  illustrated,  $4.00 

PAMELY,   C.      Colliery  Manager's   Handbook.      A 

Comprehensive  treatise  on  the  Laying-out  and 
Working  of  Collieries.  Designed  as  a  book 
of  reference  for  colliery  managers  and  for 
the  use  of  eoal-mining  students  preparing  for 
first-class  certificates.  Fifth  Edition,  revised 
and  enlarged.  Containing  over  1,000  dia- 
grams, plans,  and  engravings.  8vo,  cloth, 
illustrated  net,  $10.00 

PARR,  G.  D.  A.  Electrical  Engineering  Measur- 
ing Instruments,  for  Commercial  and  Labora- 
tory Purposes.  With  370  diagrams  and  en- 
gravings. 8vo,  cloth,  illustrated,  net,  $3.50 

PARRY,  E.  J.,  H.Sc.     The  Chemistry  of  Essential 

Oils  and  Artificial  Perfumes.  Being  an  at- 
tempt to  group  together  the  more  important 
of  the  published  facts  connected  with  the  sub- 
ject; also  giving  an  outline  of  the  principles 
involved  in  the  preparation  and  analysis  of 
Essential  Oils.  With  numerous  diagrams  and 
tables.  8vo,  cloth,  illustrated  net,  $5.00 

and    COSTE,   J.   H.      Chemistry   of   Pigments. 

With  tables  and  figures.     8vo,  cloth,  net,  $4.50 

L.  A.,  M.D.  The  Risk  and  Dangers  of  Vari- 
ous Occupations  and  their  Prevention.  A  book 
that  should  be  in  the  hands  of  manufacturers, 
the  medical  profession,  sanitary  inspectors, 
medical  officers  of  health,  managers  of  works, 
foremen  and  workmen.  8vo,  cloth,  net,  $3.00 

PARSHAL.L,,  H.  F.,  and  HOBART,  H.  M.  Arma- 
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full-page  plates,  65  tables  and  165  pages  of 
descriptive  letter-press.  4to,  cloth  ....$7.50 

Electric  Railway  Engineering.  With  num- 
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cloth,    463    pp.,    illus net,    $10.00 

This  is  undoubtedly  the  most  comprehensive 


SCIENTIFIC   PUBLICATIONS.  45 


work  on  a  rapidly  growing-  and  immensely  im- 
portant branch  of  engineering,  and  is  likely 
to  remain  for  long  the  standard  book  on  the 
subject. 

and    PARRY,    K.       Electrical    Equipment    of 

Tramways    In  Press. 

PASSMORE,     A.     €.       Handbook      of      Technical 

Terms  used  in  Architecture  and  Building,  and 
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SCIENTIFIC  PUBUCAflONS.  47 


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50  D.   VAN    NOSTRAND   COMPANY'S 


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RANKINE,  W.  J.  M.  Applied  Mechanics.  Com- 
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SCIENTIFIC   PUBLICATIONS.  51 


The  Steam-engine  and   Other  Prime   Movers. 

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and    BAMBER,    E.    F.,    C.E.      A    Mechanical 

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RATEAU,    A.      Experimental    Researches    on   the 

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52  D.    VAN    NOSTRAND   COMPANY'S 


•  its  many  varieties.  It  contains  the  recipes  for 
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SCIENTIFIC  PUBLICATIONS.  53 


N.      Faults    in    the    Manufacture    of    Woolen 

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RIPPER,  W.  A  Course  of  Instruction  in  Ma- 
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cal Engineering,  (Preliminary  Grade.)  A  series 
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ond Year  Students  of  Electrical  Engineering. 
With  Figures,  Diagrams  and  Tables.  8vo, 
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ROBERTSON,  L.   S.     Water-tube  Boilers.     Based 

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versity College,  London.  With  upward  of 
170  illustrations  and  diagrams.  8vo,  cloth,  il- 
lustrated   $3.00 

ROBINSON,  J.  B.  A  New  System  of  Architectur- 
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S.    W.      Practical    Treatise    on    the    Teeth    of 

Wheels,  with  the  theory  and  the  use  of  Rob- 
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ROEBLING,  J.  A.  Long  and  Short  Span  Rail- 
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ROLLINS,  W.  Notes  on  X-Light.  With  152  full- 
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54  D.   VAN    NOSTRAND   COMPANY'S 


ROSE,  J.,    M.K.      The   Pattern -makers'  Assistant. 

Embracing  Lathe  Work,  Branch  "Work,  Core 
Work,  Sweep  Work  and  Practical  Gear  Con- 
structions, the  Preparation  and  Use  of  Tools, 
together  with  a  large  collection  of  useful  and 
valuable  Tables.  Ninth  Edition.  With  250 
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Key    to     Engines     and    Engine-running.       A 

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ROWAN,    P.    J.      The    Practical    Physics    of    the 

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SABINE,  R.  History  and  Progress  of  the  Elec- 
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SAELTZER,  A.  Treatise  on  Acoustics  in  Con- 
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PUBLICATIONS.  SS 


SANFORD,  P.  G.     Nitro-explosives.     A  Practical 

Treatise  concerning  the  Properties,  Manufac- 
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cluding- the  Fulminates,  Smokeless  Powders 
and  Celluloid.  Second  Edition,  revised  and 
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SAUNDERS,  C.  H.  Handbook  of  Practical  Me- 
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SCHELLEN,  H.,  Dr.  Magneto-electric  and  Dyna- 
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SCHMAL.L,  C.  N.  First  Course  in  Analytic  Ge- 
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SCHMEER,  Louis.  Flow  of  Water:  A  New  The- 
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Series  of  Tables  and  Formulae  for  Dimensions 
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56  D.  VAN  NOSTRAND  COMPANY^ 


SCHWEIZER,   V.      Distillation   of  Resins,   Resin- 

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Pigments  for  Typewriting  Machines,  Manifold- 
ers,  etc.  A  description  of  the  proper  methods 
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SCIENCE  SERIES,  The  Van  Nostrand.    (Follows 

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SCRIBNER,    J.    M.       Engineers'    and    Mechanics' 

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SEATON,  A.  E.  A  Manual  of  Marine  Engineer- 
ing. Comprising  the  Designing,  Construction 
and  Working  of  Marine  Machinery.  With 
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revised  throughout,  with  an  additional  chapter 
on  Water-tube  Boilers.  8vo,  cloth  $6.00 

and  ROITNTHWAITE,  H.  M.     A  Pocket-hook 

of  Marine  Engineering  Rules  and  Tables.  For 
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SEIDELL,,   A.      (Bureau  of  Chemistry,  Wash.,  D. 

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SEVER,  G.  F.,  Prof.  Electric  Engineering  Ex- 
periments and  Tests  on  Direct-current  Ma- 
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^PUBLICATION'S.  57 


edition,  revised  and  enlarged.  8vo  pamphlet, 
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and  TOWNSEND,  F.  Laboratory  and  Fac- 
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SEW  ALL,,    C.    II.      "Wireless    Telegraphy.      With 

diagrams  and  engravings.  Second  Edition, 
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Lessons  in  Telegraphy.  For  use  as  a  Text- 
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SEWELL,  T.  Elements  of  Electrical  Engineer- 
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The    Construction    of   Dynamos    (Alternating 

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SEXTON,  A.  H.     Fuel  and  Refractory  Materials. 

8vo,   cloth    $2 . 00 

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SEYMOUR,     A.       Practical     Lithography.       With 

figures  and  engravings.  8vo,  cloth,  illustrated. 
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SHAW,  P.  E.     A  First-year  Course   of  Practical 

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Chemistry  of  the  Several  Natural  and  Arti- 
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8vo,  cloth  net,  $5  00 


58  B.   VAN    NOStfcAND 


SHELDON,  S.,  Ph.D.,  and  MASON,  H.,  B.S.  Dy- 
namo-electric Machinery:  its  Construction,  De- 
sign and  Operation,  Direct-current  Machines, 
Sixth  Edition,  revised.  8vo,  cloth,  illustrated, 
net,  f 2 . 50 

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second  volume  of  the  author's  "Dynamo-elec- 
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(Binding  uniform  with  volume  I.)  Fifth  Edi- 
t^on.  8vo,  cloth,  illustrated net,  $2.50 

SHIELDS,  J.  E.  Notes  on  Engineering  Con- 
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terial employed  in  Tunneling,  Bridging,  Canal 
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SHOCK,    W.    H.      Steam    Boilers:    their    Design, 

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Bridges  and  Roofs.  Comprising  the  determin- 
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Horizontal,  Inclined  or  Rafter,  Triangular, 
Bow-string,  Lenticular  and  other  Trusses, 
from  fixed  and  moving  loads,  with  practical 
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Students  and  Engineers.  87  woodcut  illustra- 
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SHI  Mv,  W.  F.      The  Field  Engineer.      A   Handy 

Book  of  practice  in  the  Survey,  Location  and 
Track-work  of  Railroads,  containing  a  large 
collection  of  Rules  and  Tables,  original  and 
selected,  applicable  to  both  the  Standard  and 
Narrow  Gauge,  and  prepared  with  special  ref- 
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Eighteenth  Edition,  revised  and  enlarged. 
With  addenda.  12mo,  morocco,  tucks  ...$2.50 

SIMMS,  F.  W.     A  Treatise  on  the  Principles  and 

Practice  of  Leveling.  Showing  its  application 
to  purposes  of  Railway  Engineering,  and  the 
Construction  of  Roads,  etc.  Revised  and  cor- 
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Practical  Tunneling.  Fourth  Edition.  Re- 
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Kinnear  Clark.  With  36  plates  and  other  il- 
lustrations. Imperial  8vo,  cloth  $8.00 


SCIENTIFIC  PUBLICATIONS.  59 


SIMPSON,   G.      The   Naval   Constructor.      A   Vade 

Mecum  of  Ship  Design,  for  Students,  Naval 
Architects,  Ship  Builders  and  Owners,  Marine 
Superintendents,  Engineers  and  Draughtsmen. 
12mo,  morocco,  illustrated.  500  pages,  net,  $5.00 

SINCLAIR,  ANGUS.,  Mem.  Am.  Soc.  Mech.  Eng'rs. 

Development  of  the  Locomotive  Engine.  Be- 
ing a  history  of  the  growth  of  the  locomotive 
from  the  most  elemental  forms,  with  biograph- 
ical sketches  of  the  eminent  engineers  and 
inventors.  Half  leather $5.00 

SINDALL,  R.  W.     Paper  Technology.     8vo,  cloth, 

158    illus.,    253    pp net,    $4.00 

SLATER,  J.  W.      Sewage  Treatment,  Purification 

and  Utilization.  A  Practical  Manual  for  the 
Use  of  Corporations,  Local  Boards,  Medical 
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Chemists,  Manufacturers,  Riparian  Owners, 
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SMITH,  F.  E.     Handbook  of  General  Instruction 

for  Mechanics.  Rules  and  formulae  for  prac- 
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1.  W.,  C.  E.      The  Theory   of  Ibeflections  and 

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ments of  Railway  Tracks.  Illustrated.  16mo, 
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Handbook  for  Paint  Manufacturers,  Merchants 
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W.  Chemistry  of  Hat  Manufacturing;  Lec- 
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SNELL,    A.     T.         Electric     Motive     Power;     The 

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tricity to  Mining  Work.  Second  Edition.  8vo, 
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SNOW,    W.    G    and    NOLAN,    T.      Ventilation    of 

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60  D.    VAN    NOSTRAND   COMPANY'S 


SOTHERN,  J.  W.     The  Marine  Steam  Turbine.     A 

practical  description  of  the  Parsons  Steam 
Turbine  as  presently  constructed,  fitted,  and 
run,  including  a  description  of  the  Denny  and 
Johnson  Patent  Torsion  Meter  for  measuring 
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ond Edition.  8vo,  cloth,  illus.,  163  pp.  ..$2.50 

SOXHL.ET,   D.   H.      Art    of   Dyeing    and    Staining 

Marble,  Artificial  Stone,  Bone,  Horn,  Ivory  and 
Wood,  and  of  imitating  all  sorts  of  Wood.  A 
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and  Umbrella  Makers,  Comb  Makers,  etc. 
Translated  from  the  German  by  Arthur  Mor- 
ris and  Herbert  Robson,  B.Sc.  8vo,  cloth,  170 
pages net,  $2 . 50 

SPANG,  H.  W.  A  Practical  Treatise  on  Light- 
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SPEYERS,  C.  L..  Text-book  of  Physical  Chem- 
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STAHL,   A.  W^  and  WOODS,   A.   T.      Elementary 

Mechanism.  A  Text-book  for  Students  of  Me- 
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cloth  $2 . 00 

STAL.EY,  C.,  and  PIERSON,  G.   S.     The   Separate 

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With  chapter  on  Sewage  Disposal.  With 
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STANDAGE,     H.     €.       L,eatherworkers»     Manual: 

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Agglutinants   of  all   Kinds   for  all   Purposes. 

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STEWART,    A.       Modern    Polyphase    Machinery. 

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R.  "W.     Text-book  of  Heat.     Illustrated.  8vo, 

cloth      .  « « $1,00 


SCIENTIFIC  PUBLICATIONS.  61 


Text-book  of  Magnetism  and  Electricity.  160 

Illustrations  and  numerous  examples.  12mo, 
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STILES,  A.  Tables  for  Field  Engineers.  De- 
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any  required  Degree.  Also,  Tables  of  Natural 
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STIL.LMAN,  P.      Steam-engine   Indicator  and  the 

Improved  Manometer  Steam  and  Vacuum 
Gauges;  their  Utility  and  Application.  New 
Edition.  12mo,  flexible  cloth  $1.00 

STODOLA,    Dr.    A.       Steam    Turbines.      With    an 

appendix  on  Gas  Turbines,  and  the  future  of 
Heat  Engines.  Authorized  translation  by  Dr. 
Louis  C.  Loewenstein  (Lehigh  University). 
With  241  cuts  and  3  lithographed  tables.  8vo, 
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STONE,  HERBERT,  F.L.S.,  F.R.C.I.     The  Timbers 

of  Commerce  and  their  Identification.  With 
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R.,     Gen'l.       New     Roads     and     Road     Laws 

in  the  United  States.  200  pages,  with  num- 
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STONE Y,  B.  D.  The  Theory  of  Stresses  in  Gir- 
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and  5  folding-plates.  8vo,  cloth  $12.50 

SUFFICING,  E.  R.     Treatise  on  the  Art  of  Glass 

Painting.  Prefaced  with  a  Review  of  Ancient 
Glass.  With  engravings  and  colored  plates. 
8vo,.  cloth  net,  $3 . 50 

SWEET,  S.  H.     Special  Report  on  Coal,  Showing 

its  Distribution,  Classification,  and  Costs  de- 
livered over  Different  Routes  to  Various 
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Principal  Cities  on  the  Atlantic  Coast.  With 

maps.     8vo,  cloth   $3 . 00 

SWOOPE.  C.  W.  Practical  Lessons  in  Electric- 
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SCIENTIFIC   PUBLICATIONS.  69 

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A  Practical  Description  of  the  Edison  Sys- 
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No.   60.   STRENGTH  OF  WROUGHT-IRON 

Bridge  Members.     By  S.  W.  Robinson,  C.E. 

No.  61.  POTABLE  WATER,  AND   METHODS   OF 

Detecting  Impurities,  By  M.  N.  Baker.  Sec- 
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Doug-aid  Clerk.  Third  edition.  With  addi- 
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No.   63.   HOUSE-DRAINAGE       AND       SANITARY 

Plumbing.  By  W.  P.  Gerhard.  Twelfth  edi- 
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Places  of  Decimals.  Including  Logarithms 
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No.   66.   DYNAMO-ELECTRIC    MACHINERY.      By 

S.  P.  Thompson.  With  an  Introduction  by 
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No.  67.   HYDRAULIC    TABLES    FOR    THE    CAL- 

culation  of  the  Discharge  through  Sewers, 
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No.  68.   STEAM-HEATING.       By    Robert    Brigg*. 

Third  edition,  revised,  with  additions  by 
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No.  69.  CHEMICAL   PROBLEMS.     By  Prof.  J.   C. 

Foye.  Fourth  edition,  revised  and  en- 
larged. 

No.  70.  EXPLOSIVE      MATERIALS.       By     Lieut. 

John  P.  Wisser. 

No.  71.  DYNAMIC      ELECTRICITY.         By      John 

Hopkinson,  J.  N.  Shoolbred,  and  R.  E.  Day. 

No.  72.   TOPOGRAPHICAL         SURVEYING.         By 

George  J.  Specht,  Prof.  A.  S.  Hardy,  John  B. 
McMaster,  and  H.  F.  Walling.  Third  Edition, 
revised. 

No.  73.  SYMBOLIC  ALGEBRA;  OR,  THE  ALGE- 

bra  of  Algebraic  Numbers.  By  Prof.  Wil- 
liam Cain. 

No.   74.'  TESTING       MACHINES:       THEIR       HIS- 

tory,  Construction  and  Use.  By  Arthur  V. 
Abbott. 


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No.   75.   RECENT       PROGRESS        IN       DYNAMO- 

electric  Machines.  Being1  a  Supplement  to 
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Sylvanus  P.  Thompson. 

No.  76.  MODERN   REPRODUCTIVE   GRAPHIC 

Processes.     By  Lieut.  James  S.  Pettit,  U.S.A. 

No.  77.   STADIA    SURVEYING.       The    Theory    of 

Stadia  Measurements.  By  Arthur  Winslow. 
Sixth  edition. 

No.  78.  THE          STEAM-ENGINE         INDICATOR 

and  Its  Use.     By  W.  B.  Le  Van. 

No.  79.  THE  FIGURE  OF  THE  EARTH.   By 

Frank  C.  Roberts,   C.E. 

No.  80.  HEALTHY  FOUNDATIONS  FOR 

Houses.      By   Glenn   Brown. 

No.  81.  WATER    METERS:    COMPARATIVE 

Tests  of  Accuracy,  Delivery,  etc.  Distinc- 
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Browne. 

No.   82.  THE    PRESERVATION    OF    TIMBER   BY 

the  Use  of  Antiseptics.  By  Samuel  Bagster 
Boulton,  C.E. 

No.  83.   MECHANICAL,  INTEGRATORS.  By  Prof. 

Henry  S.  H.   Shaw,  C.E. 

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nels,  Pipes,  Conduits,  Sewers,  etc.  With  Ta- 
bles. By  P.  J.  Flynn,  C.E. 

No.  85.  THE      LUMINIFEROUS       AETHER.       By 

Prof.    De   Volson   Wood. 

No.   86.  HANDBOOK      OF      MINERALOGY:      DE- 

termination,  Description,  and  Classification 
of  Minerals  Found  in  the  United  States.  By 
Prof.  J.  C.  Foye.  Fifth  edition,  revised. 

No.  87.  TREATISE  ON  THE  THEORY  OF  THE 

Construction  of  Helicoidal  Oblique  Arches. 
By  John  L.  Culley,  C.E. 

No.  88.  BEAMS   AND   GIRDERS.     Practical  For- 

mulas  for  their  Resistance.  By  P.  H.  Phil- 
brick. 

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facture,  Properties,  and  Analyses.  By  Lieut. 
John  P.  Wisser,  U.S.A. 

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the  Gyroscope.     By  Major  J.  G.  Barnard. 


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metric,  and  Spirit.  By  Prof.  I.  O.  Baker. 
Second  edition. 

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Use.     By  Boverton  Redwood,   F.I.G.,  F.C.S. 

No.   03.   RECENT     PRACTICE     IN     THE     SANI- 

tary  Drainage  of  Buildings.  With  Memo- 
randa on  the  Cost  of  Plumbing  Work.  Sec- 
ond edition,  revised  and  enlarged.  By  Wil- 
liam Paul  Gerhard,  C.E. 

No.  04.   THE    TREATMENT    OF     SEWAGE.       By 

Dr.    C.    Meymott    Tidy. 

No.   05.   PLATE-GIRDER     CONSTRUCTION.       By 

Isami  Hiroi,  C.E.     Fourth  edition,  revised. 

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By  Gisbet  Kapp,  Assoc.  M.  Inst.,  C.E. 

No.  07.  THE        DISPOSAL         OF        HOUSEHOLD 

Wastes.  Second  edition.  By  W.  Paul  Ger- 
hard, Sanitary  Engineer. 

No.  08.  PRACTICAL     DYNAMO-BUILDING    FOR 

Amateurs.  How  to  Wind  for  Any  Output. 
By  Frederick  Walker.  Fully  illustrated. 
Third  edition. 

No.  00.  TRIPLE-EXPANSION       ENGINES       AND 

Engine  Trials.  By  Prof.  Osborne  Reynolds. 
Edited  with  notes,  etc.,  by  F.  E.  Idell,  M.E. 

No.   100.  HOW  TO  BECOME  AN  ENGINEER;  or, 

The  Theoretical  and  Practical  Training  nec- 
essary in  Fitting  for  the  Duties  of  the  Civil 
Engineer.  By  Prof.  Geo.  W.  Plympton. 

No.  101.  THE    SEXTANT,    and    Other    Reflecting 

Mathematical    Instruments.      With    Practical 
'  Hints  for  their^  Adjustment  and  Use.     By  F. 
R.  Brainard,  U.  S.  Navy. 

No.  102.  THE     GALVANIC     CIRCUIT     INVESTI- 

gated  Mathematically.  By  Dr.  G.  S.  Ohm, 
Berlin,  1827.  Translated  by  William  Fran- 
cis. With  Preface  and  Notes  by  the  Editor, 
Thomas  D.  Lockwood,  M.I.E.E.  Second  edi- 
tion. 

No.   103.  THE   MICROSCOPICAL    EXAMINATION 

of  Potable  Water.  With  Diagrams.  By  Geo. 
W.  Rafter.  Second  edition. 

No.  104.  VAN  NOSTRAND'S  TABLE-BOOK  FOR 

Civil  and  Mechanical  Engineers.  Compiled 
by  Prof.  Geo.  W.  Plympton. 


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No.   105.   DETERMINANTS.      An    Introduction    to 

the  Study  of,  with  Examples  and  Applica- 
tions. By  Prof.  G.  A.  Miller. 

No.   106.   COMPRESSED  AIR.     Experiments  upon 

the  Transmission  of  Power  by  Compressed 
Air  in  Paris.  (Popp's  System.)  By  Prof. 
A.  B.  W.  Kennedy.  The  Transmission  and 
Distribution  of  Power  from  Central  Stations 
by  Compressed  Air.  By  Prof.  W.  C.  Unwin. 
Edited  by  F.  E.  Idell.  Third  edition. 

No.   107.  A   GRAPHICAL,   METHOD   FOR    SWING 

Bridges.  A  Rational  and  Easy  Graphical 
Analysis  of  the  Stresses  in  Ordinary  Swing- 
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La  Rue. 

No.   108.   SLIDE-VALVE   DIAGRAMS.      A   French 

Method  for  Constructing  Slide-valve  Dia- 
grams. By  Lloyd  Bankson,  B.S.,  Assistant 
Naval  Constructor,  U.  S.  Navy.  8  Folding 
Plates. 

No.  109.  THE  MEASUREMENT  OF  ELECTRIC 

Currents.  Electrical  Measuring  Instruments. 
By  James  Swinburne.  Meters  for  Electrical 
Energy.  By  C.  H.  Wordingham.  Edited, 
with  Preface,  by  T.  Commerford  Martin. 
With  Folding  Plate  and  Numerous  Illustra- 
tions. 

No.   110.  TRANSITION    CURVES.      A    Field-book 

for  Engineers,  Containing  Rules  and  Tables 
for  Laying  out  Transition  Curves.  By  Wal- 
ter G.  Fox,  C.E.  Second  edition. 

No.   111.   GAS-LIGHTING      AND       GAS-FITTING. 

Specifications  and  Rules  for  Gas-piping. 
Notes  on  the  Advantages  of  Gas  for  Cook- 
ing and  Heating,  and  Useful  Hints  to  Gas 
Consumers.  Third  edition.  By  Wm.  Paul 
Gerhard,  C.E. 

No.   112.  A    PRIMER    ON    THE    CALCULUS.      By 

E.  Sherman  Gould,  M.  Am.   Soc.  C.  E.     Third 
edition,   revised  and  enlarged. 

No.  113.  PHYSICAL,  PROBLEMS  and  Their  So- 
lution. By  A.  Bourgougnon,  formerly  As- 
sistant at  Bellevue  Hospital.  Second  ed. 

No.   114.  USE       OF       THE       SLIDE       RULE.       By 

F.  A.    Halsey,    of   the    "American   Machinist." 
Fourth  edition,   revised  and  enlarged. 


THE;  VAN  ^OS'I'RAND  SCIENCE  SERIES. 

No.   115.   TRAVERSE  TABLE.      Showing  therl  • 

ference   of  Latitude   and   Departure   for1" 
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Quarter    Degrees   Between    1    Degree    ai  .£ 
Degrees.      (Reprinted  from  Scribner's  P<  *; 
Table   Book.) 

No.   116.  WORM    AND    SPIRAL,    GEARING.     '2.J! 

printed   from    "American   Machinist."      B  ft 
A.     Halsey.       Second     revised    and     enla 
edition.  -»  > 

No.   117.  PRACTICAL        HYDROSTATICS,       .    i 

Hydrostatic    Formulas.      With    Numerou. 
lustrative  Figures  and  Numerical  Exam;  • 
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with  Diagrams  and  Figures.  By  Geo.  $ 
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No.   119.  LAY-OUT  OP  CORLISS  VALVE  GE, 

With     Folding-     Plates     and     Diagrams. 
Sanford     A.     Moss,     M.S.,     Ph.D.       Repri 
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sions  and  additions.     Second  edition. 

No.    120.   ART  OF   GENERATING  GEAR  TEE 

By  Howard  A.  Coombs.  With  Figures,  1 
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No.   121.  ELEMENTS      OF      G'AS    ''ENGINE      r 

sign.     Reprint  of  a  Set  of  Notes  accompai 
ing   a   Course   of   Lectures   delivered   at   C 
nell     University     in     1902.       By     Sanford 
Moss.      Illustrated. 

No.   122.   SHAFT    GOVERNORS.       By    W.    Trii 

and    C.    Housum.      Illustrated.  t 

No.   123. 'FURNACE    DRAFT:    ITS    PRODUCT!* 

by  Mechanical  Methods.  A  Handy  Referer: 
Book,  with  figures  and  tables.  By  Willifl 
Wallace  Christie.  Illustrated.  Second  e<f 
tion,  revised. 


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